ANS-8
Answers to Selected Exercises
III. 1. Answers will vary. Pertinent counterpoints
include: Not all colleges cost a fortune. Often students who were bored in high school f ind that
they enjoy college work. Though jobs like truck- ing and construction may be relatively high-
paying, the work may be more dangerous, less enjoyable, less prestigious, and less secure than
many jobs that require a college education. The difference in earning power may also be greater
than this individual supposes. Studies consistently show that college graduates make on average
about 45 percent more than those who have only a high school diploma.
4. Answers will vary. Some pertinent counterpoints include: Although the meaning of the Second
Amendment is hotly debated, few would argue that the “right to bear arms” extends to military-style
weapons that are neither necessary for personal protection nor suitable for hunting. Moreover,
the risks of legalizing such weapons would seem to outweigh the gains. The risks of foreign inva-
sion or a breakdown of society are probably pretty remote. By contrast, the risk that such weapons
could fall into the hands of criminals or be used in Columbine-type massacres, domestic disputes,
and accidental shootings is high.
7. Answers will vary. Pertinent points that arguably weaken or refute the argument include: There is
a likelihood that legalizing hard drugs would lead to greatly increased use and addiction rates, with
all the personal and societal costs this would en- tail: more overdoses, hospitalizations, car accidents,
industrial accidents, suicides, family break-ups, unemployable workers, lower productivity, and so
forth. Legalizing hard drugs would also likely make these drugs more readily available to children and
implicitly send a message that these drugs aren’t harmful.
C
HAPTER
9
E
XERCISE
9.1
1.
Artichokes Fruits
4.
Skateboarders Jazz fans
X 9. [Thus, it is ridiculous to say that drugs should be
legalized because drug use is escalating from 7 and 8.]
10. Common sense and state experiments with the decriminalization of marijuana in the 1970s tell us
that when there are fewer controls, there will be more incidents.
11. America’s two favorite legal drugs—alcohol and nicotine—have a tremendous negative impact on
the physiological, social, psychological, economic, and spiritual aspects of our lives.
12. Thus, if drugs were legalized, hospitalizations, crimes, car accidents, addicted babies, industrial
accidents, family break-ups, and other problems affiicting our society would worsen significantly.
from 10 and 11 13. [Therefore, drugs should not be legalized from 2,
6, 9, and 12.]
C
HAPTER
8
E
XERCISE
8.3
I. 1. The statement is self-refuting. If no statements are
true, then the statement that no statements are true isn’t true either. So, if the statement is true, it’s
false, which is a contradiction. 4. The statement is self-refuting. If no beliefs are jus-
tified, then the belief that no beliefs are justified isn’t justified either. So, if the statement is true,
it’s false, which is contradictory. Looked at another way, if we should be absolute and total skeptics
i.e., hold that no beliefs are justified, we should be skeptical of the claim that we should be absolute
and total skeptics, and hence not be absolute and total skeptics. The statement asserts that we should
be absolute and total skeptics, yet implies that we shouldn’t, which is contradictory.
7. If the claim here is that all children in Lake Wobegon are above average with respect to other
Lake Wobegon children, the claim is necessarily false, for something can be above average in a compari-
son group only if some other things in the group are below average. The statement is not necessarily
false if it means that all children in Lake Wobegon are above the national average.
II. 1. What about polar bears, seals, walruses, and orcas,
to name a few? 4.
Plausible counterexamples include Thoreau, Melville, Hawthorne, Poe, Fitzgerald, Hemingway,
and Faulkner, among others. 7. Don’t forget good ol’ Ohio and Utah.
Answers to Selected Exercises
ANS-9
4. Some bankers are vegetarians. No anarchists are bankers.
So, some anarchists are not vegetarians. Bankers
Anarchists Vegetarians
X
Invalid
7. No poker players are early-risers. Some firefighters are early-risers.
So, some firefighters are not poker players. Early–risers
Firefighters Poker players
X
Valid
10. No Fords are Pontiacs. All Escorts are Fords.
So, some Escorts are not Pontiacs. Fords
Escorts Pontiacs
Invalid
13. No landlubbers are sailors. Some sailors are not pirates.
So, some pirates are not landlubbers. Sailors
Pirates Landlubbers
Invalid
X
16. No fish are reptiles. All trout are fish.
So, some trout are not reptiles. Fish
Trout Reptiles
Invalid
7.
Women U.S. presidents or vice presidents
10.
Worlds greatest golfers South Americans
X
E
XERCISE
9.2
1. All psychiatrists are doctors. 4. All Mustangs are Fords.
7. All players due to report on Monday are persons who are pitchers or catchers.
10. All persons who may use the Teachers’ Lounge are teachers.
13. All persons God loves are persons that dwelleth in wisdom.
E
XERCISE
9.3
I. 1. All maples are trees.
4. All insects are animals. 7. Some things that glitter are not gold things.
10. All persons that hit are persons who swing the
bat. 13. Some birds are birds that cannot f ly. Or: Some
birds are not things that f ly. 16. All places where the grass is greener are places on
the other side. 19. Some polar bears are bears that live in Canada.
22. All liars are thieves. 25. Most humans are humans who live lives of quiet
desperation. 28. All persons who persevere in error are fools.
31. All statements that are certain are statements iden- tical to the statement “Nothing is certain.”
34. All villains dwelling in Denmark are arrant knaves.
E
XERCISE
9.4
I. 1. No barracuda are pets.
No sharks are barracuda. So, no sharks are pets.
Barracuda
Sharks Pets
Invalid
ANS-10
Answers to Selected Exercises Political scientists
Persons who favor campaign finance reform
Social scientists
Valid
X
13. All tax evaders are lawbreakers. No lawbreakers are model citizens.
So, no model citizens are tax evaders. Lawbreakers
Model citizens Tax evaders
Valid
16. No harmless acts are immoral acts. Some lies are not harmless acts.
So, some lies are not immoral acts. Harmless acts
Lies Immoral acts
Invalid
X
19. All persons who eat pizza every night are persons at risk for heart disease.
Some persons who are at risk for heart disease are cab drivers.
So, some cab drivers are persons who eat pizza every night.
Persons at risk for heart disease
Cab drivers Persons who eat
pizza every night
Invalid
X
C
HAPTER
10
E
XERCISE
10.1
I. II.
III. 1. p
1. T 1. T
4. p q 4. T
4. T 7. p q
7. F 7. F
10. p q 10. F
10. T
19. Some butchers are not bakers. No butchers are candlestick makers.
So, some candlestick makers are not bakers. Butchers
C andlestick makers
B akers
X
Invalid
II. 1. No Nobel Prize winners are rock stars.
Some astrophysicists are Nobel Prize winners. Therefore, some astrophysicists are not rock stars.
Nobel Prize winners
Astrophysicists Rock stars
Valid
X
4. All liberals are big spenders. All persons identical to Senator Crumley are big
spenders. So, all persons identical to Senator Crumley are
liberals. Big spenders
Senator Crumley Liberals
Invalid
7. Some lawyers are not golfers. All lawyers are persons who have attended law
school. So, some persons who have attended law school are
not golfers. Lawyers
Persons who have attended law school
Golfers
Valid
X
10. All political scientists are social scientists. Some political scientists are persons who favor
campaign finance reform. So, some persons who favor campaign finance
reform are social scientists.
Answers to Selected Exercises
ANS-11
V. 1. ˜ p ˜ q
... ˜ p q
p q
˜p ˜q
p q ˜p ˜q ˜p q C
T T
F F
T F
F T
F F
T F
F T
F T
T F
F F
T F
F T
T F
T T
Valid. 4. ˜ p q
p ... ˜ q
p q
p q ˜p q
p ˜q C
T T
T F
T F
T F
F T
T T
F T
F T
F F
F F
F T
F T
Valid.
E
X E R C I S E
10 .4
I. 1. T
4. F 7. T
10. T
III. 1.
c d ˜ k 4.
t b ˜ w
IV. 1.
p q ˜ q r
... ˜ r
p q
r q r
p q ˜q r
˜r C 1.
T T
T T
T F
F 2.
T T
F F
T T
T 3.
T F
T F
F T
F 4.
T F
F F
F T
T 5.
F T
T T
F F
F 6.
F T
F F
F T
T 7.
F F
T F
F T
F 8.
F F
F F
F T
T
Valid. 4.
b ˜ t ˜ m b
... ˜ m ˜ t
E
X E R C I S E
10 .2
I. 1.
p q
p q C T
T T
T F
F F
T F
F F
F
Valid. 4.
r s C
T T
T F
F T
F F
Invalid.
II. 1.
p q
... p q
p q
p q C T
T T
T F
F F
T F
F F
F
Valid.
E
X E R C I S E
10 .3
I. III.
1. F 1.
p ˜ q 4. F
4. ˜ p q 7. F
7. p ˜ q
10. T 10. ˜ p q
IV. 1.
p q
˜p ˜p q C
T T
F F
T F
F F
F T
T T
F F
T F
Valid. 4.
p q
p q ˜p q
p ˜q C
T T
T F
T F
T F
F T
T T
F T
F T
F F
F F
F T
F T
Valid.
ANS-12
Answers to Selected Exercises 4.
t a
w ˜t
t a ˜t a a v w ˜t a C 1.
T T
T F
T F
T F
2. T
T F
F T
F T
F 3.
T F
T F
F T
T F
4. T
F F
F F
T F
F 5.
F T
T T
F T
T T
6. F
T F
T F
T T
T 7.
F F
T T
F T
T F
8. F
F F
T F
T F
F
Invalid. V.
1. d v r
˜ r ... d
d r
d v r ˜r
d C T
T T
F T
T F
T T
T F
T T
F F
F F
F T
F
Valid. 4.
s v a ˜ s a
a ... s
s a
s a s v a
˜s a a
s C T
T T
T F
T T
T F
F T
T F
T F
T F
T T
T F
F F
F F
T F
F
Invalid.
E
X E R C I S E
10 .6
I. 1. F
4. T 7. F
10. T
III. 1.
b
→
e 4.
h
→
f 7. ˜ c
→
˜ e 10.
s
→
g
→
˜ s
→
p
IV. 1.
p q
p → q ˜p
˜q C 1.
T T
T F
F 2.
T F
F F
T 3.
F T
T T
F 4.
F F
T T
T
Invalid.
b m t ˜m ˜t m b b ˜t ˜m b ˜m ˜t C 1. T T T
F F
T F
F F
2. T T F F
T T
T F
F 3. T F T T
F F
F T
F 4. T F F
T T
F T
T T
5. F T T F
F F
F T
F 6. F T F
F T
F F
T F
7. F F T T F
F F
T F
8. F F F T
T F
F T
T
Valid.
V. 1.
f t ˜ s
... ˜ f s
f t
s f s
f t ˜s
˜ f sC 1.
T T
T T
T F
F 2.
T T
F F
T T
T 3.
T F
T T
F F
F 4.
T F
F F
F T
T 5.
F T
T F
F F
T 6.
F T
F F
F T
T 7.
F F
T F
F F
T 8.
F F
F F
F T
T
Valid. 4.
s ˜ e ˜ e t
... s t
s e
t ˜e
e t s ˜e ˜e t s t C 1.
T T
T F
T F
F T
2. T
T F
F F
F T
F 3.
T F
T T
F T
T T
4. T
F F
T F
T T
F 5.
F T
T F
T F
F F
6. F
T F
F F
F T
F 7.
F F
T T
F F
T F
8. F
F F
T F
F T
F
Invalid.
E
X E R C I S E
10 .5
I. III.
1. T 1.
d v r 4. T
4. w v d
7. T 7.
p v f 10. F
10. ˜ t v a w
IV. 1.
p q
p v q ˜p
q C T
T T
F T
T F
T F
F F
T T
T T
F F
F T
F
Valid.
