The Power of Logic 5th Edition by Howard-Snyder – Test Bank

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The Power of Logic 5th Edition by Howard-Snyder – Test Bank

6
Student: ___________________________________________________________________________
1. The predicate term of the conclusion in a standard form categorical syllogism is called the
A. major premise.
B. minor term.
C. middle premise.
D. major term.
2. Which of the following is not required in order for a categorical syllogism to be in standard form?
A. The premises and the conclusion are true.
B. The first premise contains the major term.
C. The second premise contains the minor term.
D. The conclusion is stated last.
3. The mood of a standard-form categorical syllogism whose major premise is universal affirmative, minor
premise is particular affirmative, and conclusion is particular affirmative would be
A. IAI.
B. IIA.
C. AII.
D. III.
4. The figure of a standard-form categorical syllogism whose middle term is the subject term of the major
premise and subject term of the minor premise would be
A. 1.
B. 2.
C. 3.
D. 4.
5. The form of a categorical syllogism is completely specified by
A. its mood.
B. its figure and mood.
C. its figure.
D. its mood, figure, and validity.
6. Which of the following categorical syllogisms is in standard form?
A. All dogs are mammals.
Cats are not dogs.
So, no cats are mammals.
B. All dogs are mammals.
No fish are mammals.
So, no dogs are fish.
C. Some mammals are small.
No whales are small.
So, no whales are mammals.
D. No whales are mammals.
Some whales are fish.
So, some fish are not mammals.
7. Identify the mood and figure of this standard-form categorical syllogism:
Some turncoats are not confederate soldiers.
No confederate soldiers are abolitionists.
So, some turncoats are abolitionists.
A. OEI-4
B. OEI-1
C. IEO-1
D. IAO-4
8. Identify the mood and figure of this standard-form categorical syllogism:
All excellent teachers are people who care about students.
All University 101 instructors are people who care about students.
So, all University 101 instructors are excellent teachers.
A. AAA-3
B. AAA-2
C. EEE-2
D. EEE-3
9. The Venn diagram representation of “All sailors are pirates” is which of the following?
A.
B.
C.
D.
10. The Venn diagram representation of “No sailors are pirates” is which of the following?
A.
B.
C.
D.
11. The Venn diagram representation of “Some sailors are pirates” is which of the following?
A.
B.
C.
D.
12. The Venn diagram representation of “Some sailors are not pirates” is which of the following?
A.
B.
C.
D.
13. Identify the Venn diagram representation of the following syllogism:
All minerals are rocks.
All diamonds are rocks.
So, all minerals are diamonds.
A.
B.
C.
D.
14. Identify the Venn diagram representation of the following syllogism:
Some ultraviolet radiation is not harmful to humans.
All ultraviolet radiation is a carcinogen.
So, some carcinogens are not harmful to humans.
A.
B.
C.
D.
15. Identify the Venn diagram representation of the following syllogism:
Some violinists are percussionists.
Some trombonists are percussionists.
So, some trombonists are violinists.
A.
B.
C.
D.
16. A categorical statement has existential import if and only if
A. it is a particular statement.
B. it implies that one of its terms denotes a nonempty class.
C. it implies that its subject term denotes a nonempty class.
D. it has importance for the nature of human existence.
17. Which of the following relations on the Square of Opposition is valid, according to modern categorical
logic?
A. contradictories
B. subcontraries
C. subalterns/subalternation
D. contraries
18. Which of the following immediate inferences is invalid according to modern categorical logic?
A. conversion
B. obversion
C. contraposition
D. contraposition by limitation
19. An enthymeme is an argument that
A. is found to be valid when tested with a Venn diagram.
B. has missing or unstated steps.
C. is a standard form categorical syllogism.
D. has the mood and figure AAA-1.
20. When supplying unstated steps, the principles of fairness and charity require that we
A. make the invalidity of the argument more apparent.
B. add only true (or at least plausible) steps.
C. supply premises that would improve the argument.
D. not make any critical remarks.
21. Which of the following is not a feature of standard-form sorites?
A. Each statement in the argument is a standard-form categorical statement.
B. Each premise (except the first) has a term in common with the immediately preceding premise.
C. The predicate term of the conclusion occurs in the last premise.
D. Each term appears twice—once in each of two different statements.
22. A sorites is
A. a chain of syllogisms in which the final conclusion is stated but the subconclusions are unstated.
B. an argument with an unstated premise or an unstated conclusion.
C. an argument comprised entirely of categorical statements.
D. a chain of inferences moving from the particular to the general.
23. When removing term-complements, which of the following is not a permissible change?
A. changing “No S are P” to “No P are S”
B. changing “All S are P” to “Some P are S”
C. changing “Some S are not P” to “Some non-P are not non-S”
D. changing “Some S are P” to “Some S are not non-P”
24. When removing term-complements, which of the following is a permissible change?
A. changing “Some S are P” to “Some non-P are non-S”
B. changing “All S are P” to “Some P are S”
C. changing “Some S are not P” to “Some non-P are not non-S”
D. changing “No S are P” to “Some S are not P”
25. A term is distributed in a statement when
A. it occurs in the subject position.
B. it occurs in the predicate position.
C. the statement says something about every member of its class.
D. the statement denies something about its class.
26. A fallacy of the undistributed middle is a violation of which of the following rules for evaluating
categorical syllogisms? In a valid standard-form categorical syllogism¼
A.
there are exactly three terms, and each term must be used with the same meaning throughout the
argument.
B. the middle term is distributed in at least one premise.
C. a term must be distributed in the premises if it is distributed in the conclusion.
D. if the conclusion is particular, then at least one of the premises must be particular.
27. A fallacy of illicit minor is a violation of which of the following rules for evaluating categorical
syllogisms? In a valid standard-form categorical syllogism¼
A.
there are exactly three terms, and each term must be used with the same meaning throughout the
argument.
B. the middle term is distributed in at least one premise.
C. a term must be distributed in the premises if it is distributed in the conclusion.
D. if the conclusion is particular, then at least one of the premises must be particular.
28. Which fallacy is committed by the following categorical syllogism?
All cats are soft and furry animals.
Some amphibians are not soft and furry animals.
So, no cats are amphibians.
A. fallacy of the undistributed middle
B. fallacy of the illicit middle
C. fallacy of the illicit major
D. fallacy of the illicit minor
29. The predicate term of the conclusion is the major term of a standard form categorical syllogism.
True False
30. The term that occurs once in each premise is called the bridge term.
True False
31. The minor term is the subject term of the conclusion.
True False
32. In a standard-form categorical syllogism, the minor premise always comes first.
True False
33. In a standard-form categorical syllogism, the conclusion always comes last.
True False
34. The figure of a standard-form categorical syllogism indicates the position of the middle term.
True False
35. The mood of a standard-form categorical syllogism is an indicator of the position of the middle term in
the premises.
True False
36. Two different categorical syllogisms cannot have the same mood and figure.
True False
37. The form of a categorical syllogism is completely specified by its mood and figure.
True False
38. To show that an area of a Venn diagram is empty, we use an “x” in that area.
True False
39. When an area of a Venn diagram is shaded, it indicates that there is at least one thing in that area.
True False
40. When a syllogism contains both a universal and a particular premise, you should always diagram the
universal first.
True False
41. A categorical statement has existential import when (and only when) it implies that its subject terms only
denote classes that have at least one member (i.e., are nonempty).
True False
42. Aristotelian and modern logicians agree that universal categorical statements have existential import.
True False
43. According to modern logicians, “All elves are people with infrared vision” is equivalent to “If anything is
an elf, then it is a person with infrared vision.”
True False
44. The only relationship on the Square of Opposition that both Aristotelian and modern logicians accept is
contradictories.
True False
45. An enthymeme is an argument with a true conclusion.
True False
46. All enthymemes are valid.
True False
47. When forced to choose between adding a false premise and making an enthymeme clearly invalid, we
adopt the practice of adding a false premise and thereby making the syllogism valid.
True False
48. A sorites is a chain of syllogisms in which the final conclusion is stated but the subconclusions are
unstated.
True False
49. In a standard form sorites, the subject term of the conclusion must occur in the first premise.
True False
50. Evaluating the validity of a sorites requires that we identify all its subconclusions.
True False
51. When reducing the number of terms (removing term complements) in a categorical syllogism, we are not
permitted to use conversion by limitation nor contraposition by limitation.
True False
52. The only requirement when removing term complements is that the changes we make to each statement
must produce a logically equivalent statement.
True False
53. A term is distributed in a categorical statement if the statement says something about every member of
the class that term denotes.
True False
54. In “Some dogs are mammals,” the subject term is distributed.
True False
55. In a universal negative statement, both terms are distributed.
True False
56. In a valid standard-form categorical syllogism, the middle term must be distributed in at least one
premise.
True False
57. Any categorical syllogism with two negative premises is invalid.
True False
58. Any categorical syllogism with two affirmative premises is valid.
True False
59. From the standpoint of modern logic, a valid standard-form categorical syllogism with a particular
conclusion can have two universal premises.
True False
60. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: All hyperventilating iguanas are bungee-jumpers since all bungee-jumpers are pencil-pushers and
some pencil-pushers are hyperventilating iguanas.
61. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: No drowsy dromedaries are prized prodigies since all prized prodigies are shameless sheiks and no
shameless sheiks are drowsy dromedaries.
62. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: No tragic actors are idiots. But some comedians are not idiots. So, some comedians are not tragic
actors.
63. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: No coal tar derivatives are nourishing foods, because all artificial dyes are coal tar derivatives and
no artificial dyes are nourishing foods.
64. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Some spaniels are not good hunters, though all spaniels are gentle dogs. Thus, no gentle dogs are
good hunters.
65. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: All professional wrestlers are good actors, because some good actors are not powerful athletes and
all professional wrestlers are powerful athletes.
66. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: All patriotic citizens are mindless followers of the government, and all soldiers are mindless
followers of the government, so all soldiers are patriotic citizens.
67. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Since some science professors are absent-minded persons and all philosophers are absent-minded
persons, some scientists are not philosophers.
68. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: No knights are shrubberies, since no shrubberies are jousters and all jousters are knights.
69. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Whereas all Klingon warriors are ferocious opponents and some Klingon warriors are not male, it
must be that some ferocious opponents are not males.
70. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Some tax-exempt organizations are religious associations and no tax-exempt organizations are
profitable businesses. Thus, some religious associations are not profitable businesses.
71. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Since all aardvarks are CB radio operators, and no CB radio operators are Olympic champions, no
Olympic champions are aardvarks.
72. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Some Tibetan monks are bookstore junkies, because no Ronald Reagan movie fans are bookstore
junkies and some Tibetan monks are Ronald Reagan movie fans.
73. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: All cartographers are Martians from outer space, and some cartographers are not agents for the
CIA, whence it follows that some agents for the CIA are not Martians from outer space.
74. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Some Swedish water volleyball team members are not beer drinkers, because some molecular
biologists are Swedish water volleyball team members and some molecular biologists are not beer
drinkers.
75. The following categorical argument form has more than three terms: “Some non-P are non-M. All non-S
are M. So, some S are not P.” Reduce the terms to three by removing term-complements via applications
of conversion, obversion, and/or contraposition.
76. The following categorical argument form has more than three terms: “No non-M are P. Some S are non-
M. So, no S are non-P.” Reduce the terms to three by removing term-complements via applications of
conversion, obversion, and/or contraposition.
77. The following categorical argument form has more than three terms: “No non-P are non-M. Some M are
non-S. So, some S are P.” Reduce the terms to three by removing term-complements via applications of
conversion, obversion, and/or contraposition.
78. The following categorical argument form has more than three terms: “All non-P are M. Some S are non-
M. So, no non-S are P.” Reduce the terms to three by removing term-complements via applications of
conversion, obversion, and/or contraposition.
79. The following categorical argument form has more than three terms: “All P are M. Some non-S are M.
So, no non-S are non-P.” Reduce the terms to three by removing term-complements via applications of
conversion, obversion, and/or contraposition.
80. Which of the five rules for evaluating syllogisms can you use to determine whether the following form is
valid?
All M are P.
No S are M.
So, no S are P.
81. Which of the five rules for evaluating syllogisms can you use to determine whether the following form is
valid?
All M are P.
All M are S.
Some S are not P.
82. Which of the five rules for evaluating syllogisms can you use to determine whether the following form is
valid?
No M are P.
No S are M.
All S are P.
83. Which of the five rules for evaluating syllogisms can you use to determine whether the following form is
valid?
All P are M.
Some S are M.
So, some S are not P.
84. Which of the five rules for evaluating syllogisms can you use to determine whether the following form is
valid?
All M are P.
All M are S.
So, all S are P.
85. Put the following categorical syllogism into standard form and identify its mood and figure.
No Romulans are Members of the Federation. This is because all Members of the federation are peaceful
races and all Romulans are peaceful races.
86. Put the following categorical syllogism into standard form and identify its mood and figure.
Whereas all Klingon warriors are ferocious opponents and some Klingon warriors are not male, it must be
that some ferocious opponents are not males.
87. Put the following categorical syllogism into standard form and identify its mood and figure.
No Starships are Ferengi inventions because all Warp-capable ships are Starships and no Ferengi
inventions are Warp-capable ships.
88. Put the following categorical syllogism into standard form and identify its mood and figure.
Because some Makhi are Lieutenants in the Federation and no criminals are Makhi, some Lieutenants in
the Federation are not criminals.
89. Put the following categorical syllogism into standard form and identify its mood and figure.
Some shuttle-craft are not ships with shields because some scientific vessels are shuttle-craft and some
scientific vessels are not ships with shields.
90. Put the following categorical syllogism into standard form and identify its mood and figure.
All snakes are cold-blooded animals, so some snakes are egg-layers since some cold-blooded animals are
egg-layers.
91. Put the following categorical syllogism into standard form and identify its mood and figure.
No tragic actors are idiots. But some comedians are not idiots. So, some comedians are not tragic
actors.
92. Put the following categorical syllogism into standard form and identify its mood and figure.
Some diamonds are not precious stones and some carbon compounds are not diamonds. Thus, some
carbon compounds are not precious stones.
93. Put the following categorical syllogism into standard form and identify its mood and figure.
No coal tar derivatives are nourishing foods, because all artificial dyes are coal tar derivatives and no
artificial dyes are nourishing foods.
94. Put the following categorical syllogism into standard form and identify its mood and figure.
Some parrots are not pests. All parrots are pets. Thus, no pets are pests.
95. Put the following categorical syllogism into standard form and identify its mood and figure.
All criminal actions are wicked deeds. All prosecutions for murder are criminal actions. Thus, all
prosecutions for murder are wicked deeds.
96. Put the following categorical syllogism into standard form and identify its mood and figure.
No writers of lewd and sensational articles are honest and decent citizens, but some journalists are not
writers of lewd and sensational articles; consequently some journalists are honest and decent citizens.
97. Put the following categorical syllogism into standard form and identify its mood and figure.
Some spaniels are not good hunters, though all spaniels are gentle dogs. Thus, no gentle dogs are good
hunters.
98. Put the following categorical syllogism into standard form and identify its mood and figure.
All professional wrestlers are good actors, because some good actors are not powerful athletes and all
professional wrestlers are powerful athletes.
99. Put the following categorical syllogism into standard form and identify its mood and figure.
All storm troopers are metalheads, so some storm troopers are not ballet afficionados, since some ballet
afficionados are metalheads.
100.Put the following categorical syllogism into standard form and identify its mood and figure.
No reticulocytes are leukocytes, but all phagocytic cells are reticulocytes. Whence it follows that no
phagocytic cells are leukocytes.
101.Put the following categorical syllogism into standard form and identify its mood and figure.
Some calyculated planets are high-orbiting satellites. But some zoantharians are calyculated planets, since
some high-orbiting satellites are zoantharians.
102.Put the following categorical syllogism into standard form and identify its mood and figure.
No Shoshoneans are Tylezian mud-dobbers, but all Shoshoneans are quixotic members of the Uto-
Aztecan phylum. So, some Tylezian mud-dobbers are quixotic members of the Uto-Aztecan phylum.
103.Put the following categorical syllogism into standard form and identify its mood and figure.
Some Necromonicons are Talmudic doctrines, given that all Linneaen manuscripts are Necromonicons
and some Talmudic doctrines are Linneaen manuscripts.
104.Put the following categorical syllogism into standard form and identify its mood and figure.
Since no hobbits are grand wizards and some grand wizards are members of the Circle of Seven, it
follows that some members of the Circle of Seven are not hobbits.
105.Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
Because all whales are mammals, at least some aquatic animals are mammals.
106.Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
No fallacies are valid arguments, since no valid arguments are mistakes in reasoning.
107.Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
Since all chickens are egg-layers, it follows that no chickens are mammals.
108.Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
All psychics are frauds, because all psychics are people who make false claims about their abilities.
109.Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
It must be that some tabloid reporters are gossipmongers because all overzealous journalists are tabloid
reporters.
110.Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
Some arguments are sound arguments because some arguments are valid arguments and all valid
arguments are sound arguments.
6 Key
1. The predicate term of the conclusion in a standard form categorical syllogism is called the
A. major premise.
B. minor term.
C. middle premise.
D. major term.
Howard – Chapter 06 #1
Subject area: 6.1 Standard Form, Mood, and Figure
2. Which of the following is not required in order for a categorical syllogism to be in standard form?
A. The premises and the conclusion are true.
B. The first premise contains the major term.
C. The second premise contains the minor term.
D. The conclusion is stated last.
Howard – Chapter 06 #2
Subject area: 6.1 Standard Form, Mood, and Figure
3. The mood of a standard-form categorical syllogism whose major premise is universal affirmative,
minor premise is particular affirmative, and conclusion is particular affirmative would be
A. IAI.
B. IIA.
C. AII.
D. III.
Howard – Chapter 06 #3
Subject area: 6.1 Standard Form, Mood, and Figure
4. The figure of a standard-form categorical syllogism whose middle term is the subject term of the
major premise and subject term of the minor premise would be
A. 1.
B. 2.
C. 3.
D. 4.
Howard – Chapter 06 #4
Subject area: 6.1 Standard Form, Mood, and Figure
5. The form of a categorical syllogism is completely specified by
A. its mood.
B. its figure and mood.
C. its figure.
D. its mood, figure, and validity.
Howard – Chapter 06 #5
Subject area: 6.1 Standard Form, Mood, and Figure
6. Which of the following categorical syllogisms is in standard form?
A. All dogs are mammals.
Cats are not dogs.
So, no cats are mammals.
B. All dogs are mammals.
No fish are mammals.
So, no dogs are fish.
C. Some mammals are small.
No whales are small.
So, no whales are mammals.
D. No whales are mammals.
Some whales are fish.
So, some fish are not mammals.
Howard – Chapter 06 #6
Subject area: 6.1 Standard Form, Mood, and Figure
7. Identify the mood and figure of this standard-form categorical syllogism:
Some turncoats are not confederate soldiers.
No confederate soldiers are abolitionists.
So, some turncoats are abolitionists.
A. OEI-4
B. OEI-1
C. IEO-1
D. IAO-4
Howard – Chapter 06 #7
Subject area: 6.1 Standard Form, Mood, and Figure
8. Identify the mood and figure of this standard-form categorical syllogism:
All excellent teachers are people who care about students.
All University 101 instructors are people who care about students.
So, all University 101 instructors are excellent teachers.
A. AAA-3
B. AAA-2
C. EEE-2
D. EEE-3
Howard – Chapter 06 #8
Subject area: 6.1 Standard Form, Mood, and Figure
9. The Venn diagram representation of “All sailors are pirates” is which of the following?
A.
B.
C.
D.
Howard – Chapter 06 #9
Subject area: 6.2 Venn Diagrams and Categorical Statements
10. The Venn diagram representation of “No sailors are pirates” is which of the following?
A.
B.
C.
D.
Howard – Chapter 06 #10
Subject area: 6.2 Venn Diagrams and Categorical Statements
11. The Venn diagram representation of “Some sailors are pirates” is which of the following?
A.
B.
C.
D.
Howard – Chapter 06 #11
Subject area: 6.2 Venn Diagrams and Categorical Statements
12. The Venn diagram representation of “Some sailors are not pirates” is which of the following?
A.
B.
C.
D.
Howard – Chapter 06 #12
Subject area: 6.2 Venn Diagrams and Categorical Statements
13. Identify the Venn diagram representation of the following syllogism:
All minerals are rocks.
All diamonds are rocks.
So, all minerals are diamonds.
A.
B.
C.
D.
Howard – Chapter 06 #13
Subject area: 6.3 Venn Diagrams and Categorical Syllogisms
14. Identify the Venn diagram representation of the following syllogism:
Some ultraviolet radiation is not harmful to humans.
All ultraviolet radiation is a carcinogen.
So, some carcinogens are not harmful to humans.
A.
B.
C.
D.
Howard – Chapter 06 #14
Subject area: 6.3 Venn Diagrams and Categorical Syllogisms
15. Identify the Venn diagram representation of the following syllogism:
Some violinists are percussionists.
Some trombonists are percussionists.
So, some trombonists are violinists.
A.
B.
C.
D.
Howard – Chapter 06 #15
Subject area: 6.3 Venn Diagrams and Categorical Syllogisms
16. A categorical statement has existential import if and only if
A. it is a particular statement.
B. it implies that one of its terms denotes a nonempty class.
C. it implies that its subject term denotes a nonempty class.
D. it has importance for the nature of human existence.
Howard – Chapter 06 #16
Subject area: 6.4 The Modern Square of Opposition
17. Which of the following relations on the Square of Opposition is valid, according to modern
categorical logic?
A. contradictories
B. subcontraries
C. subalterns/subalternation
D. contraries
Howard – Chapter 06 #17
Subject area: 6.4 The Modern Square of Opposition
18. Which of the following immediate inferences is invalid according to modern categorical logic?
A. conversion
B. obversion
C. contraposition
D. contraposition by limitation
Howard – Chapter 06 #18
Subject area: The Modern Square of Opposition
19. An enthymeme is an argument that
A. is found to be valid when tested with a Venn diagram.
B. has missing or unstated steps.
C. is a standard form categorical syllogism.
D. has the mood and figure AAA-1.
Howard – Chapter 06 #19
Subject area: 6.5 Enthymemes
20. When supplying unstated steps, the principles of fairness and charity require that we
A. make the invalidity of the argument more apparent.
B. add only true (or at least plausible) steps.
C. supply premises that would improve the argument.
D. not make any critical remarks.
Howard – Chapter 06 #20
Subject area: 6.5 Enthymemes
21. Which of the following is not a feature of standard-form sorites?
A. Each statement in the argument is a standard-form categorical statement.
B. Each premise (except the first) has a term in common with the immediately preceding premise.
C. The predicate term of the conclusion occurs in the last premise.
D. Each term appears twice—once in each of two different statements.
Howard – Chapter 06 #21
Subject area: 6.6 Sorites and Removing Term-Complements
22. A sorites is
A. a chain of syllogisms in which the final conclusion is stated but the subconclusions are unstated.
B. an argument with an unstated premise or an unstated conclusion.
C. an argument comprised entirely of categorical statements.
D. a chain of inferences moving from the particular to the general.
Howard – Chapter 06 #22
Subject area: 6.6 Sorites and Removing Term-Complements
23. When removing term-complements, which of the following is not a permissible change?
A. changing “No S are P” to “No P are S”
B. changing “All S are P” to “Some P are S”
C. changing “Some S are not P” to “Some non-P are not non-S”
D. changing “Some S are P” to “Some S are not non-P”
Howard – Chapter 06 #23
Subject area: 6.6 Sorites and Removing Term-Complements
24. When removing term-complements, which of the following is a permissible change?
A. changing “Some S are P” to “Some non-P are non-S”
B. changing “All S are P” to “Some P are S”
C. changing “Some S are not P” to “Some non-P are not non-S”
D. changing “No S are P” to “Some S are not P”
Howard – Chapter 06 #24
Subject area: 6.6 Sorites and Removing Term-Complements
25. A term is distributed in a statement when
A. it occurs in the subject position.
B. it occurs in the predicate position.
C. the statement says something about every member of its class.
D. the statement denies something about its class.
Howard – Chapter 06 #25
Subject area: 6.7 Rules for Evaluating Syllogisms
26. A fallacy of the undistributed middle is a violation of which of the following rules for evaluating
categorical syllogisms? In a valid standard-form categorical syllogism¼
A.
there are exactly three terms, and each term must be used with the same meaning throughout the
argument.
B. the middle term is distributed in at least one premise.
C. a term must be distributed in the premises if it is distributed in the conclusion.
D. if the conclusion is particular, then at least one of the premises must be particular.
Howard – Chapter 06 #26
Subject area: 6.7 Rules for Evaluating Syllogisms
27. A fallacy of illicit minor is a violation of which of the following rules for evaluating categorical
syllogisms? In a valid standard-form categorical syllogism¼
A.
there are exactly three terms, and each term must be used with the same meaning throughout the
argument.
B. the middle term is distributed in at least one premise.
C. a term must be distributed in the premises if it is distributed in the conclusion.
D. if the conclusion is particular, then at least one of the premises must be particular.
Howard – Chapter 06 #27
Subject area: 6.7 Rules for Evaluating Syllogisms
28. Which fallacy is committed by the following categorical syllogism?
All cats are soft and furry animals.
Some amphibians are not soft and furry animals.
So, no cats are amphibians.
A. fallacy of the undistributed middle
B. fallacy of the illicit middle
C. fallacy of the illicit major
D. fallacy of the illicit minor
Howard – Chapter 06 #28
Subject area: 6.7 Rules for Evaluating Syllogisms
29. The predicate term of the conclusion is the major term of a standard form categorical syllogism.
TRUE
Howard – Chapter 06 #29
Subject area: 6.1 Standard Form, Mood, and Figure
30. The term that occurs once in each premise is called the bridge term.
FALSE
Howard – Chapter 06 #30
Subject area: 6.1 Standard Form, Mood, and Figure
31. The minor term is the subject term of the conclusion.
TRUE
Howard – Chapter 06 #31
Subject area: 6.1 Standard Form, Mood, and Figure
32. In a standard-form categorical syllogism, the minor premise always comes first.
FALSE
Howard – Chapter 06 #32
Subject area: 6.1 Standard Form, Mood, and Figure
33. In a standard-form categorical syllogism, the conclusion always comes last.
TRUE
Howard – Chapter 06 #33
34. The figure of a standard-form categorical syllogism indicates the position of the middle term.
TRUE
Howard – Chapter 06 #34
Subject area: 6.1 Standard Form, Mood, and Figure
35. The mood of a standard-form categorical syllogism is an indicator of the position of the middle term in
the premises.
FALSE
Howard – Chapter 06 #35
Subject area: 6.1 Standard Form, Mood, and Figure
36. Two different categorical syllogisms cannot have the same mood and figure.
FALSE
Howard – Chapter 06 #36
Subject area: 6.1 Standard Form, Mood, and Figure
37. The form of a categorical syllogism is completely specified by its mood and figure.
TRUE
Howard – Chapter 06 #37
Subject area: 6.1 Standard Form, Mood, and Figure
38. To show that an area of a Venn diagram is empty, we use an “x” in that area.
FALSE
Howard – Chapter 06 #38
Subject area: 6.2 Venn Diagrams and Categorical Statements
39. When an area of a Venn diagram is shaded, it indicates that there is at least one thing in that area.
FALSE
Howard – Chapter 06 #39
Subject area: 6.2 Venn Diagrams and Categorical Statements
40. When a syllogism contains both a universal and a particular premise, you should always diagram the
universal first.
TRUE
Howard – Chapter 06 #40
Subject area: 6.3 Venn Diagrams and Categorical Syllogisms
41. A categorical statement has existential import when (and only when) it implies that its subject terms
only denote classes that have at least one member (i.e., are nonempty).
TRUE
Howard – Chapter 06 #41
Subject area: 6.4 The Modern Square of Opposition
42. Aristotelian and modern logicians agree that universal categorical statements have existential
import.
FALSE
Howard – Chapter 06 #42
Subject area: 6.4 The Modern Square of Opposition
43. According to modern logicians, “All elves are people with infrared vision” is equivalent to “If
anything is an elf, then it is a person with infrared vision.”
TRUE
Howard – Chapter 06 #43
Subject area: 6.4 The Modern Square of Opposition
44. The only relationship on the Square of Opposition that both Aristotelian and modern logicians accept
is contradictories.
TRUE
Howard – Chapter 06 #44
Subject area: 6.4 The Modern Square of Opposition
45. An enthymeme is an argument with a true conclusion.
FALSE
Howard – Chapter 06 #45
Subject area: 6.5 Enthymemes
46. All enthymemes are valid.
FALSE
Howard – Chapter 06 #46
Subject area: 6.5 Enthymemes
47. When forced to choose between adding a false premise and making an enthymeme clearly invalid, we
adopt the practice of adding a false premise and thereby making the syllogism valid.
TRUE
Howard – Chapter 06 #47
Subject area: 6.5 Enthymemes
48. A sorites is a chain of syllogisms in which the final conclusion is stated but the subconclusions are
unstated.
TRUE
Howard – Chapter 06 #48
Subject area: 6.6 Sorites and Removing Term-Complements
49. In a standard form sorites, the subject term of the conclusion must occur in the first premise.
FALSE
Howard – Chapter 06 #49
Subject area: 6.6 Sorites and Removing Term-Complements
50. Evaluating the validity of a sorites requires that we identify all its subconclusions.
TRUE
Howard – Chapter 06 #50
Subject area: 6.6 Sorites and Removing Term-Complements
51. When reducing the number of terms (removing term complements) in a categorical syllogism, we are
not permitted to use conversion by limitation nor contraposition by limitation.
TRUE
Howard – Chapter 06 #51
Subject area: 6.6 Sorites and Removing Term-Complements
52. The only requirement when removing term complements is that the changes we make to each
statement must produce a logically equivalent statement.
TRUE
Howard – Chapter 06 #52
Subject area: 6.6 Sorites and Removing Term-Complements
53. A term is distributed in a categorical statement if the statement says something about every member of
the class that term denotes.
TRUE
Howard – Chapter 06 #53
Subject area: 6.7 Rules for Evaluating Syllogisms
54. In “Some dogs are mammals,” the subject term is distributed.
FALSE
Howard – Chapter 06 #54
Subject area: 6.7 Rules for Evaluating Syllogisms
55. In a universal negative statement, both terms are distributed.
TRUE
Howard – Chapter 06 #55
Subject area: 6.7 Rules for Evaluating Syllogisms
56. In a valid standard-form categorical syllogism, the middle term must be distributed in at least one
premise.
TRUE
Howard – Chapter 06 #56
Subject area: 6.7 Rules for Evaluating Syllogisms
57. Any categorical syllogism with two negative premises is invalid.
TRUE
Howard – Chapter 06 #57
Subject area: 6.7 Rules for Evaluating Syllogisms
58. Any categorical syllogism with two affirmative premises is valid.
FALSE
Howard – Chapter 06 #58
Subject area: 6.7 Rules for Evaluating Syllogisms
59. From the standpoint of modern logic, a valid standard-form categorical syllogism with a particular
conclusion can have two universal premises.
FALSE
Howard – Chapter 06 #59
Subject area: 6.7 Rules for Evaluating Syllogisms
60. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: All hyperventilating iguanas are bungee-jumpers since all bungee-jumpers are pencil-pushers
and some pencil-pushers are hyperventilating iguanas.
AIA-4
Howard – Chapter 06 #60
Subject area: Putting syllogisms into standard form
61. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: No drowsy dromedaries are prized prodigies since all prized prodigies are shameless sheiks
and no shameless sheiks are drowsy dromedaries.
AEE-4
Howard – Chapter 06 #61
Subject area: Putting syllogisms into standard form
62. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: No tragic actors are idiots. But some comedians are not idiots. So, some comedians are not
tragic actors.
EOO-2
Howard – Chapter 06 #62
Subject area: Putting syllogisms into standard form
63. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: No coal tar derivatives are nourishing foods, because all artificial dyes are coal tar derivatives
and no artificial dyes are nourishing foods.
EAE-3
Howard – Chapter 06 #63
Subject area: Putting syllogisms into standard form
64. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Some spaniels are not good hunters, though all spaniels are gentle dogs. Thus, no gentle dogs
are good hunters.
OAE-3
Howard – Chapter 06 #64
Subject area: Putting syllogisms into standard form
65. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: All professional wrestlers are good actors, because some good actors are not powerful athletes
and all professional wrestlers are powerful athletes.
OAA-2
Howard – Chapter 06 #65
Subject area: Putting syllogisms into standard form
66. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: All patriotic citizens are mindless followers of the government, and all soldiers are mindless
followers of the government, so all soldiers are patriotic citizens.
AAA-2
Howard – Chapter 06 #66
Subject area: Putting syllogisms into standard form
67. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Since some science professors are absent-minded persons and all philosophers are absentminded
persons, some scientists are not philosophers.
AIO-2
Howard – Chapter 06 #67
Subject area: Putting syllogisms into standard form
68. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: No knights are shrubberies, since no shrubberies are jousters and all jousters are knights.
EAE-4
Howard – Chapter 06 #68
Subject area: Putting syllogisms into standard form
69. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Whereas all Klingon warriors are ferocious opponents and some Klingon warriors are not
male, it must be that some ferocious opponents are not males.
OAO-3
Howard – Chapter 06 #69
Subject area: Putting syllogisms into standard form
70. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Some tax-exempt organizations are religious associations and no tax-exempt organizations are
profitable businesses. Thus, some religious associations are not profitable businesses.
EIO-3
Howard – Chapter 06 #70
Subject area: Putting syllogisms into standard form
71. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Since all aardvarks are CB radio operators, and no CB radio operators are Olympic champions,
no Olympic champions are aardvarks.
AEE-4
Howard – Chapter 06 #71
Subject area: Putting syllogisms into standard form
72. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood
and figure: Some Tibetan monks are bookstore junkies, because no Ronald Reagan movie fans are
bookstore junkies and some Tibetan monks are Ronald Reagan movie fans.
EII-1
Howard – Chapter 06 #72
Subject area: Putting syllogisms into standard form
73. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: All cartographers are Martians from outer space, and some cartographers are not agents for the
CIA, whence it follows that some agents for the CIA are not Martians from outer space.
AOO-3
Howard – Chapter 06 #73
Subject area: Putting syllogisms into standard form
74. Rewrite the following argument as a standard-form categorical syllogism; then identify its mood and
figure: Some Swedish water volleyball team members are not beer drinkers, because some molecular
biologists are Swedish water volleyball team members and some molecular biologists are not beer
drinkers.
Answers will vary
Howard – Chapter 06 #74
Subject area: Putting syllogisms into standard form
75. The following categorical argument form has more than three terms: “Some non-P are non-M. All
non-S are M. So, some S are not P.” Reduce the terms to three by removing term-complements via
applications of conversion, obversion, and/or contraposition.
Some non-P are non-M.
No non-S are non-M. (obversion)
So, some non-P are not non-S. (contraposition)
Howard – Chapter 06 #75
Subject area: Removing term-complements
76. The following categorical argument form has more than three terms: “No non-M are P. Some S
are non-M. So, no S are non-P.” Reduce the terms to three by removing term-complements via
applications of conversion, obversion, and/or contraposition.
All P are M. (conversion, obversion)
Some S are not M. (obversion)
So, all S are P. (obversion)
Or:
No non-M are P.
Some S are non-M.
So, all S are P. (obversion)
Howard – Chapter 06 #76
Subject area: Removing term-complements
77. The following categorical argument form has more than three terms: “No non-P are non-M. Some
M are non-S. So, some S are P.” Reduce the terms to three by removing term-complements via
applications of conversion, obversion, and/or contraposition.
All non-P are M. (obversion)
Some M are not S. (obversion)
So, some S are not non-P. (obversion)
Howard – Chapter 06 #77
Subject area: Removing term-complements
78. The following categorical argument form has more than three terms: “All non-P are M. Some S
are non-M. So, no non-S are P.” Reduce the terms to three by removing term-complements via
applications of conversion, obversion, and/or contraposition.
No non-P are non-M. (obversion)
Some non-M are not non-S. (conversion, obversion)
So, all non-S are non-P. (obversion)
Howard – Chapter 06 #78
Subject area: Removing term-complements
79. The following categorical argument form has more than three terms: “All P are M. Some non-S are M.
So, no non-S are non-P.” Reduce the terms to three by removing term-complements via applications
of conversion, obversion, and/or contraposition.
All non-M are non-P. (contraposition)
Some non-S are not non-M. (obversion)
So, no non-S are non-P.
Or:
All P are M.
Some non-S are M.
So, all non-S are P. (obversion)
Howard – Chapter 06 #79
Subject area: Removing term-complements
80. Which of the five rules for evaluating syllogisms can you use to determine whether the following form
is valid?
All M are P.
No S are M.
So, no S are P.
Rule 3 (fallacy of illicit major)
Howard – Chapter 06 #80
Subject area: Rules for evaluating syllogisms
81. Which of the five rules for evaluating syllogisms can you use to determine whether the following form
is valid?
All M are P.
All M are S.
Some S are not P.
Rules 4 and 5
Howard – Chapter 06 #81
Subject area: Rules for evaluating syllogisms
82. Which of the five rules for evaluating syllogisms can you use to determine whether the following form
is valid?
No M are P.
No S are M.
All S are P.
Rule 4
Howard – Chapter 06 #82
Subject area: Rules for evaluating syllogisms
83. Which of the five rules for evaluating syllogisms can you use to determine whether the following form
is valid?
All P are M.
Some S are M.
So, some S are not P.
Rules 2 (fallacy of undistributed middle) and 4
Howard – Chapter 06 #83
Subject area: Rules for evaluating syllogisms
84. Which of the five rules for evaluating syllogisms can you use to determine whether the following form
is valid?
All M are P.
All M are S.
So, all S are P.
Rule 3 (fallacy of illicit minor)
Howard – Chapter 06 #84
Subject area: Rules for evaluating syllogisms
85. Put the following categorical syllogism into standard form and identify its mood and figure.
No Romulans are Members of the Federation. This is because all Members of the federation are
peaceful races and all Romulans are peaceful races.
AAE-2, invalid
Howard – Chapter 06 #85
Subject area: Venn diagrams and categorical syllogisms
86. Put the following categorical syllogism into standard form and identify its mood and figure.
Whereas all Klingon warriors are ferocious opponents and some Klingon warriors are not male, it
must be that some ferocious opponents are not males.
OAO-e, valid
Howard – Chapter 06 #86
Subject area: Venn diagrams and categorical syllogisms
87. Put the following categorical syllogism into standard form and identify its mood and figure.
No Starships are Ferengi inventions because all Warp-capable ships are Starships and no Ferengi
inventions are Warp-capable ships.
EAE-4, invalid
Howard – Chapter 06 #87
Subject area: Venn diagrams and categorical syllogisms
88. Put the following categorical syllogism into standard form and identify its mood and figure.
Because some Makhi are Lieutenants in the Federation and no criminals are Makhi, some Lieutenants
in the Federation are not criminals.
EIO-4, valid
Howard – Chapter 06 #88
Subject area: Venn diagrams and categorical syllogisms
89. Put the following categorical syllogism into standard form and identify its mood and figure.
Some shuttle-craft are not ships with shields because some scientific vessels are shuttle-craft and some
scientific vessels are not ships with shields.
OIO-2, invalid
Howard – Chapter 06 #89
Subject area: Venn diagrams and categorical syllogisms
90. Put the following categorical syllogism into standard form and identify its mood and figure.
All snakes are cold-blooded animals, so some snakes are egg-layers since some cold-blooded animals
are egg-layers.
IAI-1, invalid
Howard – Chapter 06 #90
Subject area: Venn diagrams and categorical syllogisms
91. Put the following categorical syllogism into standard form and identify its mood and figure.
No tragic actors are idiots. But some comedians are not idiots. So, some comedians are not tragic
actors.
EOO-2, invalid
Howard – Chapter 06 #91
Subject area: Venn diagrams and categorical syllogisms
92. Put the following categorical syllogism into standard form and identify its mood and figure.
Some diamonds are not precious stones and some carbon compounds are not diamonds. Thus, some
carbon compounds are not precious stones.
OOI-1, invalid
Howard – Chapter 06 #92
Subject area: Venn diagrams and categorical syllogisms
93. Put the following categorical syllogism into standard form and identify its mood and figure.
No coal tar derivatives are nourishing foods, because all artificial dyes are coal tar derivatives and no
artificial dyes are nourishing foods.
EAE-3, invalid
Howard – Chapter 06 #93
Subject area: Venn diagrams and categorical syllogisms
94. Put the following categorical syllogism into standard form and identify its mood and figure.
Some parrots are not pests. All parrots are pets. Thus, no pets are pests.
OAE-3, invalid
Howard – Chapter 06 #94
Subject area: Venn diagrams and categorical syllogisms
95. Put the following categorical syllogism into standard form and identify its mood and figure.
All criminal actions are wicked deeds. All prosecutions for murder are criminal actions. Thus, all
prosecutions for murder are wicked deeds.
AAA-1, valid
Howard – Chapter 06 #95
Subject area: Venn diagrams and categorical syllogisms
96. Put the following categorical syllogism into standard form and identify its mood and figure.
No writers of lewd and sensational articles are honest and decent citizens, but some journalists are
not writers of lewd and sensational articles; consequently some journalists are honest and decent
citizens.
EOI-1, invalid
Howard – Chapter 06 #96
Subject area: Venn diagrams and categorical syllogisms
97. Put the following categorical syllogism into standard form and identify its mood and figure.
Some spaniels are not good hunters, though all spaniels are gentle dogs. Thus, no gentle dogs are good
hunters.
OAE-3, invalid
Howard – Chapter 06 #97
Subject area: Venn diagrams and categorical syllogisms
98. Put the following categorical syllogism into standard form and identify its mood and figure.
All professional wrestlers are good actors, because some good actors are not powerful athletes and all
professional wrestlers are powerful athletes.
OAA-2, invalid
Howard – Chapter 06 #98
Subject area: Venn diagrams and categorical syllogisms
99. Put the following categorical syllogism into standard form and identify its mood and figure.
All storm troopers are metalheads, so some storm troopers are not ballet afficionados, since some
ballet afficionados are metalheads.
IAO-2, invalid
Howard – Chapter 06 #99
Subject area: Venn diagrams and categorical syllogisms
100. Put the following categorical syllogism into standard form and identify its mood and figure.
No reticulocytes are leukocytes, but all phagocytic cells are reticulocytes. Whence it follows that no
phagocytic cells are leukocytes.
EAE-1, valid
Howard – Chapter 06 #100
Subject area: Venn diagrams and categorical syllogisms
101. Put the following categorical syllogism into standard form and identify its mood and figure.
Some calyculated planets are high-orbiting satellites. But some zoantharians are calyculated planets,
since some high-orbiting satellites are zoantharians.
III-4, invalid
Howard – Chapter 06 #101
Subject area: Venn diagrams and categorical syllogisms
102. Put the following categorical syllogism into standard form and identify its mood and figure.
No Shoshoneans are Tylezian mud-dobbers, but all Shoshoneans are quixotic members of the
Uto-Aztecan phylum. So, some Tylezian mud-dobbers are quixotic members of the Uto-Aztecan
phylum.
AEI-3, invalid
Howard – Chapter 06 #102
Subject area: Venn diagrams and categorical syllogisms
103. Put the following categorical syllogism into standard form and identify its mood and figure.
Some Necromonicons are Talmudic doctrines, given that all Linneaen manuscripts are
Necromonicons and some Talmudic doctrines are Linneaen manuscripts.
IAI-4, valid
Howard – Chapter 06 #103
Subject area: Venn diagrams and categorical syllogisms
104. Put the following categorical syllogism into standard form and identify its mood and figure.
Since no hobbits are grand wizards and some grand wizards are members of the Circle of Seven, it
follows that some members of the Circle of Seven are not hobbits.
EIO-4, valid
Howard – Chapter 06 #104
Subject area: Venn diagrams and categorical syllogisms
105. Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
Because all whales are mammals, at least some aquatic animals are mammals.
All W are M.
Some A are W.
So, some A are M.
Valid
Howard – Chapter 06 #105
Subject area: Enthymemes
106. Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
No fallacies are valid arguments, since no valid arguments are mistakes in reasoning.
No V are M.
All F are M.
So, no F are V.
Valid
Howard – Chapter 06 #106
Subject area: Enthymemes
107. Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
Since all chickens are egg-layers, it follows that no chickens are mammals.
All C are E.
No E are M.
So, no C are M.
Valid
Howard – Chapter 06 #107
Subject area: Enthymemes
108. Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
All psychics are frauds, because all psychics are people who make false claims about their
abilities.
All C are F.
All P are C.
So, all P are F.
Valid
Howard – Chapter 06 #108
Subject area: Enthymemes
109. Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
It must be that some tabloid reporters are gossipmongers because all overzealous journalists are
tabloid reporters.
Answers will vary
Howard – Chapter 06 #109
Subject area: Enthymemes
110. Identify the missing step in the following argument (remember the principles of charity and fairness!
). Then put the argument into standard form. To cut down on writing, use capital letters to abbreviate
English terms.
Some arguments are sound arguments because some arguments are valid arguments and all valid
arguments are sound arguments.
Answers will vary
Howard – Chapter 06 #110
Subject area: Enthymemes
6 Summary
Category # of Questions
Howard – Chapter 06 110
Subject area: 6.1 Standard Form, Mood, and Figure 16
Subject area: 6.2 Venn Diagrams and Categorical Statements 6
Subject area: 6.3 Venn Diagrams and Categorical Syllogisms 4
Subject area: 6.4 The Modern Square of Opposition 6
Subject area: 6.5 Enthymemes 5
Subject area: 6.6 Sorites and Removing Term-Complements 9
Subject area: 6.7 Rules for Evaluating Syllogisms 11
Subject area: Enthymemes 6
Subject area: Putting syllogisms into standard form 15
Subject area: Removing term-complements 5
Subject area: Rules for evaluating syllogisms 5
Subject area: The Modern Square of Opposition 1
Subject area: Venn diagrams and categorical syllogisms 20

 

7
Student: ___________________________________________________________________________
1. In (A ⋁ B) → [B • (C ⋁ ~D)], what is the main logical operator?
A. the first occurrence of ⋁
B. •
C. →
D. the second occurrence of ⋁
2. Which of the following is an atomic statement?
A. Sailing is an enjoyable sport.
B. Sewing and cross-stitch require good eyesight.
C. The Cincinnati Reds did not win their last game.
D. Either Sue or Karen will get the high score.
3. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the
statement “Neither Fred nor Lou likes ice cream” is best symbolized by
A. ~F ⋁ ~L.
B. ~F • ~L.
C. ~F → ~L.
D. ~(F • L).
4. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the
statement “Either Fred or Lou doesn’t like ice cream” is best symbolized by
A. ~F ⋁ ~L.
B. ~F • ~L.
C. ~F → ~L.
D. ~(F • L).
5. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the statement “Fred
doesn’t like ice cream only if Lou doesn’t like ice cream” is best symbolized by
A. ~F ⋁ ~L.
B. ~F • ~L.
C. ~F → ~L.
D. ~(F • L).
6. The “⋁” sign is used to symbolize
A. “Either . . . or . . . but not both.”
B. “If . . . then . . .”
C. “Both . . . and . . .”
D. “Either . . . or . . . or both.”
7. In A → B,
A. A provides a necessary condition for B.
B. B provides a sufficient condition for A.
C. A provides a sufficient condition for B.
D. A provides both a necessary and sufficient condition for B.
8. Which of the following is not a condition for a symbolic expression to be a well-formed formula (WFF)?
A. If p is a WFF, then so is ~(p).
B. If p and q are WFFs, then so is (p • q).
C. If p and q are WFFs, then so is (p ⋁ q).
D. If p and q are WFFs, then so is (p → q).
9. Which of the following is not a well-formed formula (WFF)?
A. (~A → B ⋁ C)
B. ~A → (B ⋁ C)
C. ~(A → B) ⋁ C
D. (~A → B) ⋁ C
10. A compound statement is truth-functional if
A. more than one atomic statement is a component.
B. its truth value is a function of the content of its component atomic statement(s).
C. in most contexts it functions as a true statement.
D. its truth value is a function of the truth value of its component atomic statements.
11. On which assignment of truth values does the sentence A → ~B turn out to be false?
A. A is true, and B is true.
B. A is true, and B is false.
C. A is false, and B is true.
D. A is false, and B is false.
12. Under which assignment of truth values does the sentence A ↔ (B • ~C) turn out to be true?
A. A is true, B is false, and C is false.
B. A is false, B is true, and C is false.
C. A is false, B is false, and C is false.
D. A is true, B is false, and C is true.
13. Under which assignment of truth values does the sentence (A ↔ ~B) • ~C turn out to be true?
A. A is true, B is false, and C is false.
B. A is true, B is true, and C is false.
C. A is false, B is false, and C is false.
D. A is true, B is false, and C is true.
14. The truth table for a symbolized argument containing four statement letters will have
A. 4 rows.
B. 8 rows.
C. 12 rows.
D. 16 rows.
15. Using a truth table, we can tell that an argument is valid if
A. there is at least one row where the premises and conclusion are all true.
B. there is no row where the premises are true and the conclusion is false.
C. there is no row where the conclusion is false.
D. there is at least one row where the premises are all true and the conclusion is false.
16. A compound statement is a tautology if
A. it is false regardless of the truth values assigned to the atomic sentences that compose it.
B. its truth value is a function of the truth values of its component atomic sentences.
C. it is true regardless of the truth values assigned to its component atomic sentences.
D. its truth value is a function of the placement of its parentheses.
17. A compound statement is a contradiction if
A. it is false regardless of the truth values assigned to the atomic sentences that compose it.
B. its truth value is a function of the truth values of its component atomic sentences.
C. it is true regardless of the truth values assigned to its component atomic sentences.
D. its truth value is a function of the placement of its parentheses.
18. When two statements are logically equivalent, the columns in the truth table under their main logical
operators
A. show neither statement is contingent.
B. are exactly alike.
C. are exactly opposite.
D. show both statements are tautologies.
19. An atomic statement is a statement that has no other statement as a component.
True False
20. A compound statement is one that has at least one atomic statement as a component.
True False
21. “Chocolate is not nutritious” is an atomic statement.
True False
22. “All roses are red flowers” is a compound statement.
True False
23. In A • B, the statement constants are called disjuncts.
True False
24. The symbol for disjunction represents inclusive “or.”
True False
25. In A → B, the consequent is B.
True False
26. The statement ~A ⋁ B is a negation.
True False
27. A sufficient condition is a condition that, if lacking, guarantees that a statement is false (or that a
phenomenon will not occur).
True False
28. A necessary condition is a condition that guarantees that a statement is true (or that a phenomenon will
occur).
True False
29. The consequent of a true conditional statement provides a necessary condition for the truth of the
antecedent.
True False
30. The English phrase “if and only if” is symbolized with the “↔”.
True False
31. A statement variable is a lower case letter that serves as a placeholder for any statement.
True False
32. (A → B ⋁ C) is a well-formed formula.
True False
33. (A → (B ⋁ C) ⋁ D) is a well-formed formula.
True False
34. In A ⋁ (B • C), the main logical operator is the “⋁”.
True False
35. In (A ⋁ (B) • (D ⋁ C), the main logical operator is the “⋁”.
True False
36. A compound statement is truth functional if its truth value is completely determined by the truth value of
the atomic statements that compose it.
True False
37. A conjunction is true if either one of its conjuncts is true; otherwise, it is false.
True False
38. A disjunction is false if both its disjuncts are false; otherwise it is true.
True False
39. A material conditional is false if its antecedent is true and its consequent is false; otherwise, it is true.
True False
40. A material biconditional is true when its two constituent statements have different truth values;
otherwise, it is true.
True False
41. An argument is valid when it is not possible for its conclusion to be false when all of its premises are
true.
True False
42. The truth table for an argument that has three component atomic statements will have six rows.
True False
43. The abbreviated truth table method can be used to prove that an argument is valid.
True False
44. If there is any assignment of truth values in which the premises are all true and the conclusion is false,
then the argument is invalid.
True False
45. A tautology is a statement that is necessarily false—that is, it is false regardless of the truth values
assigned to the atomic statements that compose it.
True False
46. A statement that is false regardless of the truth values assigned to the atomic statements that compose it is
a contradiction.
True False
47. Any argument with logically inconsistent premises will be valid yet unsound.
True False
48. A statement that is true in at least one row of the truth table and false in at least one row is contingent.
True False
49. Two statements are logically equivalent when each validly implies the other.
True False
50. Two statements are logically equivalent when the biconditional connecting them is a tautology.
True False
51. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true
or false) of this compound statement: A • C
True False
52. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true
or false) of this compound statement: B • ~C
True False
53. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true
or false) of this compound statement: D ⋁ B
True False
54. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true
or false) of this compound statement: C → ~(C • B)
True False
55. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true
or false) of this compound statement: A ↔ (C ⋁ D)
True False
56. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true
or false) of this compound statement: B → ~(A • B)
True False
57. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true
or false) of this compound statement: (A • B) → (A ⋁ ~(C ⋁ B))
True False
58. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true
or false) of this compound statement: ~(A • B) ↔ (A → (C ⋁D))
True False
59. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true
or false) of this compound statement: ~(A → C) • (C ⋁ ~D)
True False
60. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value (true
or false) of this compound statement: ~(A ⋁ C) ↔ (B • ~(A ⋁ C))
True False
61. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: You can
vote in the Democratic primary election only if you are a registered member of the Democratic Party.
(V: You can vote in the Democratic primary election; R: You are a registered member of the Democratic
Party.)
62. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: It’s not the
case that Sally is in love with James, though James is in love with Sally. (S: Sally is in love with James; J:
James is in love with Sally.)
63. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: The
presence of H2O on Mars is sufficient for the production of life-forms. (H: H2O is present on Mars; P:
Life-forms are produced on Mars.)
64. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Susan will
be able to go to the graduate school of her choice unless she scores very poorly on her GRE. (C: Susan is
able to go to the graduate school of her choice; P: Susan scores very poorly on her GRE.)
65. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Unless
Sharon passes her final, she will get a C in the class. (P: Sharon passes her final; C: Sharon gets a C in the
class.)
66. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Although
Stephen scored high on the LSAT, he did not get into the law school of his choice. (S: Stephen scored
high on the LSAT; L: Stephen got into the law school of his choice.)
67. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Both Al and
Bob failed to come to the party. (A: Al came to the party; B: Bob came to the party.)
68. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Neither Jean
nor Ron is allergic to shellfish. (J: Jean is allergic to shellfish; R: Ron is allergic to shellfish.)
69. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: It is not the
case that neither ostriches nor turkeys can fly. (O: Ostriches can fly; T: Turkeys can fly.)
70. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Jones wins
only if Smith and Brown both lose. (J: Jones wins; S: Smith wins; B: Brown wins.)
71. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Assuming
that Susie is at the horse show, Dee Dee is either at home or at work. (S: Susie is at the horse show; H:
Dee Dee is at home; W: Dee Dee is at work.)
72. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: A necessary
condition for Adonis to go camping is that he behave and not bark at other dogs. (C: Adonis goes
camping; B: Adonis behaves; O: Adonis barks at other dogs.)
73. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan’s
attendance in class is both a necessary and sufficient condition for his passing this class. (A: Nathan
attends class; P: Nathan passes class.)
74. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Both
Patricia and Scott are prepared for the test, but Henry is not. (P: Patricia is prepared for the test; S: Scott
is prepared for the test; H: Henry is prepared for the test.)
75. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Either
Abigail and Dieter both go to the dance or neither does. (A: Abigail goes to the dance; D: Dieter goes to
the dance.)
76. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: It will either
rain or snow, but not both. (R: It will rain; S: It will snow.)
77. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: It will snow
if and only if it is below 32° out and the humidity is greater than 60 percent. (S: It will snow; B: It is
below 32° out; H: The humidity is greater than 60 percent.)
78. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: If there’s too
much rain in the early spring and not enough during the summer, the tomato crop will not be very good.
(S: There is too much rain in the spring; I: There is enough rain during the summer; G: The tomato crop is
very good.)
79. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: If the
argument has all true premises and a false conclusion, then the argument is not valid. (P: The argument
has all true premises; C: The argument has a true conclusion; V: The argument is valid.)
80. Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan will
go to the Cayman Islands for spring break if and only if he gets an A on his geology mid-term, finishes
his English research paper, and does not lose his job. (C: Nathan will go to the Cayman Islands for spring
break; G: Nathan gets an A on his geology midterm; E: Nathan finishes his English research paper; J:
Nathan loses his job.)

7 Key
1. In (A ⋁ B) → [B • (C ⋁ ~D)], what is the main logical operator?
A. the first occurrence of ⋁
B. •
C. →
D. the second occurrence of ⋁
Howard – Chapter 07 #1
Subject area: 7.1 Symbolizing English Arguments
2. Which of the following is an atomic statement?
A. Sailing is an enjoyable sport.
B. Sewing and cross-stitch require good eyesight.
C. The Cincinnati Reds did not win their last game.
D. Either Sue or Karen will get the high score.
Howard – Chapter 07 #2
Subject area: 7.1 Symbolizing English Arguments
3. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the
statement “Neither Fred nor Lou likes ice cream” is best symbolized by
A. ~F ⋁ ~L.
B. ~F • ~L.
C. ~F → ~L.
D. ~(F • L).
Howard – Chapter 07 #3
Subject area: 7.1 Symbolizing English Arguments
4. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the
statement “Either Fred or Lou doesn’t like ice cream” is best symbolized by
A. ~F ⋁ ~L.
B. ~F • ~L.
C. ~F → ~L.
D. ~(F • L).
Howard – Chapter 07 #4
Subject area: 7.1 Symbolizing English Arguments
5. Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the
statement “Fred doesn’t like ice cream only if Lou doesn’t like ice cream” is best symbolized by
A. ~F ⋁ ~L.
B. ~F • ~L.
C. ~F → ~L.
D. ~(F • L).
Howard – Chapter 07 #5
Subject area: 7.1 Symbolizing English Arguments
6. The “⋁” sign is used to symbolize
A. “Either . . . or . . . but not both.”
B. “If . . . then . . .”
C. “Both . . . and . . .”
D. “Either . . . or . . . or both.”
Howard – Chapter 07 #6
Subject area: 7.1 Symbolizing English Arguments
7. In A → B,
A. A provides a necessary condition for B.
B. B provides a sufficient condition for A.
C. A provides a sufficient condition for B.
D. A provides both a necessary and sufficient condition for B.
Howard – Chapter 07 #7
Subject area: 7.1 Symbolizing English Arguments
8. Which of the following is not a condition for a symbolic expression to be a well-formed formula
(WFF)?
A. If p is a WFF, then so is ~(p).
B. If p and q are WFFs, then so is (p • q).
C. If p and q are WFFs, then so is (p ⋁ q).
D. If p and q are WFFs, then so is (p → q).
Howard – Chapter 07 #8
Subject area: 7.1 Symbolizing English Arguments
9. Which of the following is not a well-formed formula (WFF)?
A. (~A → B ⋁ C)
B. ~A → (B ⋁ C)
C. ~(A → B) ⋁ C
D. (~A → B) ⋁ C
Howard – Chapter 07 #9
Subject area: 7.1 Symbolizing English Arguments
10. A compound statement is truth-functional if
A. more than one atomic statement is a component.
B. its truth value is a function of the content of its component atomic statement(s).
C. in most contexts it functions as a true statement.
D. its truth value is a function of the truth value of its component atomic statements.
Howard – Chapter 07 #10
Subject area: 7.2 Truth Tables
11. On which assignment of truth values does the sentence A → ~B turn out to be false?
A. A is true, and B is true.
B. A is true, and B is false.
C. A is false, and B is true.
D. A is false, and B is false.
Howard – Chapter 07 #11
Subject area: 7.2 Truth Tables
12. Under which assignment of truth values does the sentence A ↔ (B • ~C) turn out to be true?
A. A is true, B is false, and C is false.
B. A is false, B is true, and C is false.
C. A is false, B is false, and C is false.
D. A is true, B is false, and C is true.
Howard – Chapter 07 #12
Subject area: 7.2 Truth Tables
13. Under which assignment of truth values does the sentence (A ↔ ~B) • ~C turn out to be true?
A. A is true, B is false, and C is false.
B. A is true, B is true, and C is false.
C. A is false, B is false, and C is false.
D. A is true, B is false, and C is true.
Howard – Chapter 07 #13
Subject area: 7.2 Truth Tables
14. The truth table for a symbolized argument containing four statement letters will have
A. 4 rows.
B. 8 rows.
C. 12 rows.
D. 16 rows.
Howard – Chapter 07 #14
Subject area: 7.3 Using Truth Tables to Evaluate Arguments
15. Using a truth table, we can tell that an argument is valid if
A. there is at least one row where the premises and conclusion are all true.
B. there is no row where the premises are true and the conclusion is false.
C. there is no row where the conclusion is false.
D. there is at least one row where the premises are all true and the conclusion is false.
Howard – Chapter 07 #15
Subject area: 7.3 Using Truth Tables to Evaluate Arguments
16. A compound statement is a tautology if
A. it is false regardless of the truth values assigned to the atomic sentences that compose it.
B. its truth value is a function of the truth values of its component atomic sentences.
C. it is true regardless of the truth values assigned to its component atomic sentences.
D. its truth value is a function of the placement of its parentheses.
Howard – Chapter 07 #16
Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence
17. A compound statement is a contradiction if
A. it is false regardless of the truth values assigned to the atomic sentences that compose it.
B. its truth value is a function of the truth values of its component atomic sentences.
C. it is true regardless of the truth values assigned to its component atomic sentences.
D. its truth value is a function of the placement of its parentheses.
Howard – Chapter 07 #17
Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence
18. When two statements are logically equivalent, the columns in the truth table under their main logical
operators
A. show neither statement is contingent.
B. are exactly alike.
C. are exactly opposite.
D. show both statements are tautologies.
Howard – Chapter 07 #18
Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence
19. An atomic statement is a statement that has no other statement as a component.
TRUE
Howard – Chapter 07 #19
Subject area: 7.1 Symbolizing English Arguments
20. A compound statement is one that has at least one atomic statement as a component.
TRUE
Howard – Chapter 07 #20
Subject area: 7.1 Symbolizing English Arguments
21. “Chocolate is not nutritious” is an atomic statement.
FALSE
Howard – Chapter 07 #21
Subject area: 7.1 Symbolizing English Arguments
22. “All roses are red flowers” is a compound statement.
FALSE
Howard – Chapter 07 #22
Subject area: 7.1 Symbolizing English Arguments
23. In A • B, the statement constants are called disjuncts.
FALSE
Howard – Chapter 07 #23
Subject area: 7.1 Symbolizing English Arguments
24. The symbol for disjunction represents inclusive “or.”
TRUE
Howard – Chapter 07 #24
Subject area: 7.1 Symbolizing English Arguments
25. In A → B, the consequent is B.
TRUE
Howard – Chapter 07 #25
Subject area: 7.1 Symbolizing English Arguments
26. The statement ~A ⋁ B is a negation.
FALSE
Howard – Chapter 07 #26
Subject area: 7.1 Symbolizing English Arguments
27. A sufficient condition is a condition that, if lacking, guarantees that a statement is false (or that a
phenomenon will not occur).
FALSE
Howard – Chapter 07 #27
Subject area: 7.1 Symbolizing English Arguments
28. A necessary condition is a condition that guarantees that a statement is true (or that a phenomenon
will occur).
FALSE
Howard – Chapter 07 #28
Subject area: 7.1 Symbolizing English Arguments
29. The consequent of a true conditional statement provides a necessary condition for the truth of the
antecedent.
TRUE
Howard – Chapter 07 #29
Subject area: 7.1 Symbolizing English Arguments
30. The English phrase “if and only if” is symbolized with the “↔”.
TRUE
Howard – Chapter 07 #30
Subject area: 7.1 Symbolizing English Arguments
31. A statement variable is a lower case letter that serves as a placeholder for any statement.
TRUE
Howard – Chapter 07 #31
Subject area: 7.1 Symbolizing English Arguments
32. (A → B ⋁ C) is a well-formed formula.
FALSE
Howard – Chapter 07 #32
Subject area: 7.1 Symbolizing English Arguments
33. (A → (B ⋁ C) ⋁ D) is a well-formed formula.
FALSE
Howard – Chapter 07 #33
Subject area: 7.1 Symbolizing English Arguments
34. In A ⋁ (B • C), the main logical operator is the “⋁”.
TRUE
Howard – Chapter 07 #34
Subject area: 7.1 Symbolizing English Arguments
35. In (A ⋁ (B) • (D ⋁ C), the main logical operator is the “⋁”.
FALSE
Howard – Chapter 07 #35
Subject area: 7.1 Symbolizing English Arguments
36. A compound statement is truth functional if its truth value is completely determined by the truth value
of the atomic statements that compose it.
TRUE
Howard – Chapter 07 #36
Subject area: 7.2 Truth Tables
37. A conjunction is true if either one of its conjuncts is true; otherwise, it is false.
FALSE
Howard – Chapter 07 #37
Subject area: 7.2 Truth Tables
38. A disjunction is false if both its disjuncts are false; otherwise it is true.
TRUE
Howard – Chapter 07 #38
Subject area: 7.2 Truth Tables
39. A material conditional is false if its antecedent is true and its consequent is false; otherwise, it is
true.
TRUE
Howard – Chapter 07 #39
Subject area: 7.2 Truth Tables
40. A material biconditional is true when its two constituent statements have different truth values;
otherwise, it is true.
FALSE
Howard – Chapter 07 #40
Subject area: 7.2 Truth Tables
41. An argument is valid when it is not possible for its conclusion to be false when all of its premises are
true.
TRUE
Howard – Chapter 07 #41
Subject area: 7.3 Using Truth Tables to Evaluate Arguments
42. The truth table for an argument that has three component atomic statements will have six rows.
FALSE
Howard – Chapter 07 #42
Subject area: 7.3 Using Truth Tables to Evaluate Arguments
43. The abbreviated truth table method can be used to prove that an argument is valid.
FALSE
Howard – Chapter 07 #43
Subject area: 7.4 Abbreviated Truth Tables
44. If there is any assignment of truth values in which the premises are all true and the conclusion is false,
then the argument is invalid.
TRUE
Howard – Chapter 07 #44
Subject area: 7.4 Abbreviated Truth Tables
45. A tautology is a statement that is necessarily false—that is, it is false regardless of the truth values
assigned to the atomic statements that compose it.
FALSE
Howard – Chapter 07 #45
Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence
46. A statement that is false regardless of the truth values assigned to the atomic statements that compose
it is a contradiction.
TRUE
Howard – Chapter 07 #46
Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence
47. Any argument with logically inconsistent premises will be valid yet unsound.
TRUE
Howard – Chapter 07 #47
Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence
48. A statement that is true in at least one row of the truth table and false in at least one row is
contingent.
TRUE
Howard – Chapter 07 #48
Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence
49. Two statements are logically equivalent when each validly implies the other.
TRUE
Howard – Chapter 07 #49
Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence
50. Two statements are logically equivalent when the biconditional connecting them is a tautology.
TRUE
Howard – Chapter 07 #50
Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence
51. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value
(true or false) of this compound statement: A • C
FALSE
Howard – Chapter 07 #51
Subject area: Determining truth values
52. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value
(true or false) of this compound statement: B • ~C
TRUE
Howard – Chapter 07 #52
Subject area: Determining truth values
53. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value
(true or false) of this compound statement: D ⋁ B
TRUE
Howard – Chapter 07 #53
Subject area: Determining truth values
54. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value
(true or false) of this compound statement: C → ~(C • B)
TRUE
Howard – Chapter 07 #54
Subject area: Determining truth values
55. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value
(true or false) of this compound statement: A ↔ (C ⋁ D)
FALSE
Howard – Chapter 07 #55
Subject area: Determining truth values
56. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value
(true or false) of this compound statement: B → ~(A • B)
FALSE
Howard – Chapter 07 #56
Subject area: Determining truth values
57. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value
(true or false) of this compound statement: (A • B) → (A ⋁ ~(C ⋁ B))
TRUE
Howard – Chapter 07 #57
Subject area: Determining truth values
58. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value
(true or false) of this compound statement: ~(A • B) ↔ (A → (C ⋁D))
TRUE
Howard – Chapter 07 #58
Subject area: Determining truth values
59. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value
(true or false) of this compound statement: ~(A → C) • (C ⋁ ~D)
TRUE
Howard – Chapter 07 #59
Subject area: Determining truth values
60. Making the assumption that A is true, B is true, C is false, and D is false, determine the truth value
(true or false) of this compound statement: ~(A ⋁ C) ↔ (B • ~(A ⋁ C))
TRUE
Howard – Chapter 07 #60
Subject area: Determining truth values
61. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: You
can vote in the Democratic primary election only if you are a registered member of the Democratic
Party. (V: You can vote in the Democratic primary election; R: You are a registered member of the
Democratic Party.)
V → R
Howard – Chapter 07 #61
Subject area: Symbolizing
62. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: It’s not
the case that Sally is in love with James, though James is in love with Sally. (S: Sally is in love with
James; J: James is in love with Sally.)
~S • J
Howard – Chapter 07 #62
Subject area: Symbolizing
63. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: The
presence of H2O on Mars is sufficient for the production of life-forms. (H: H2O is present on Mars; P:
Life-forms are produced on Mars.)
H → P
Howard – Chapter 07 #63
Subject area: Symbolizing
64. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Susan
will be able to go to the graduate school of her choice unless she scores very poorly on her GRE. (C:
Susan is able to go to the graduate school of her choice; P: Susan scores very poorly on her GRE.)
C ⋁ P
Howard – Chapter 07 #64
Subject area: Symbolizing
65. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Unless
Sharon passes her final, she will get a C in the class. (P: Sharon passes her final; C: Sharon gets a C in
the class.)
C ⋁ P
Howard – Chapter 07 #65
Subject area: Symbolizing
66. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Although
Stephen scored high on the LSAT, he did not get into the law school of his choice. (S: Stephen scored
high on the LSAT; L: Stephen got into the law school of his choice.)
S • ~L
Howard – Chapter 07 #66
Subject area: Symbolizing
67. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Both Al
and Bob failed to come to the party. (A: Al came to the party; B: Bob came to the party.)
~A • ~B
Howard – Chapter 07 #67
Subject area: Symbolizing
68. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Neither
Jean nor Ron is allergic to shellfish. (J: Jean is allergic to shellfish; R: Ron is allergic to shellfish.)
~J • ~R or ~(J ⋁R)
Howard – Chapter 07 #68
Subject area: Symbolizing
69. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: It is not
the case that neither ostriches nor turkeys can fly. (O: Ostriches can fly; T: Turkeys can fly.)
~(~O • ~T)
Howard – Chapter 07 #69
Subject area: Symbolizing
70. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Jones
wins only if Smith and Brown both lose. (J: Jones wins; S: Smith wins; B: Brown wins.)
J → (~S • ~B)
Howard – Chapter 07 #70
Subject area: Symbolizing
71. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided:
Assuming that Susie is at the horse show, Dee Dee is either at home or at work. (S: Susie is at the
horse show; H: Dee Dee is at home; W: Dee Dee is at work.)
S → (H ⋁W)
Howard – Chapter 07 #71
Subject area: Symbolizing
72. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: A
necessary condition for Adonis to go camping is that he behave and not bark at other dogs. (C: Adonis
goes camping; B: Adonis behaves; O: Adonis barks at other dogs.)
C → (B • ~O)
Howard – Chapter 07 #72
Subject area: Symbolizing
73. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan’s
attendance in class is both a necessary and sufficient condition for his passing this class. (A: Nathan
attends class; P: Nathan passes class.)
A ↔ P
Howard – Chapter 07 #73
Subject area: Symbolizing
74. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Both
Patricia and Scott are prepared for the test, but Henry is not. (P: Patricia is prepared for the test; S:
Scott is prepared for the test; H: Henry is prepared for the test.)
(P • S) • ~H
Howard – Chapter 07 #74
Subject area: Symbolizing
75. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: Either
Abigail and Dieter both go to the dance or neither does. (A: Abigail goes to the dance; D: Dieter goes
to the dance.)
(A • D) ⋁ ~(A ⋁ D)
Howard – Chapter 07 #75
Subject area: Symbolizing
76. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: It will
either rain or snow, but not both. (R: It will rain; S: It will snow.)
(R ⋁ S) • ~(R • S)
Howard – Chapter 07 #76
Subject area: Symbolizing
77. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: It will
snow if and only if it is below 32° out and the humidity is greater than 60 percent. (S: It will snow; B:
It is below 32° out; H: The humidity is greater than 60 percent.)
S ↔ (B • H)
Howard – Chapter 07 #77
Subject area: Symbolizing
78. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: If there’s
too much rain in the early spring and not enough during the summer, the tomato crop will not be very
good. (S: There is too much rain in the spring; I: There is enough rain during the summer; G: The
tomato crop is very good.)
(S • ~I) → ~G
Howard – Chapter 07 #78
Subject area: Symbolizing
79. Symbols list
You may use the list below to copy-and-paste the symbols into your answer as needed.
→; ↔; •; ~; ⋁;
Translate the following statement into symbols, using the schemes of abbreviation provided: If
the argument has all true premises and a false conclusion, then the argument is not valid. (P: The
argument has all true premises; C: The argument has a true conclusion; V: The argument is valid.)
(P • ~C) → ~V
Howard – Chapter 07 #79
Subject area: Symbolizing
80. Translate the following statement into symbols, using the schemes of abbreviation provided: Nathan
will go to the Cayman Islands for spring break if and only if he gets an A on his geology mid-term,
finishes his English research paper, and does not lose his job. (C: Nathan will go to the Cayman
Islands for spring break; G: Nathan gets an A on his geology midterm; E: Nathan finishes his English
research paper; J: Nathan loses his job.)
Answers will vary
Howard – Chapter 07 #80
Subject area: Symbolizing
7 Summary
Category # of Questions
Howard – Chapter 07 80
Subject area: 7.1 Symbolizing English Arguments 26
Subject area: 7.2 Truth Tables 9
Subject area: 7.3 Using Truth Tables to Evaluate Arguments 4
Subject area: 7.4 Abbreviated Truth Tables 2
Subject area: 7.5 Tautology, Contradiction, Contingency, and Logical Equivalence 9
Subject area: Determining truth values 10
Subject area: Symbolizing 20