Chapter 09 Deductive Arguments I Answer Key
Short Answer Questions
1.
Translate the following into a standard-form categorical claim: Not every product that’s
organic is actually a chemical-free product.
Some organic products are not chemical-free products.
2.
Translate the following into a standard-form categorical claim: The only organic products
are chemical-free products.
All organic products are chemical-free products.
3.
Translate the following into a standard-form categorical claim: Chemical-free products are
the only organic products.
All organic products are chemical-free products.
4.
Translate the following into a standard-form categorical claim: Only organic products are
chemical-free products.
All chemical-free products are organic products.
5.
Translate the following into a standard-form categorical claim: Chemical-free products are
not the only organic products.
Some organic products are not chemical-free products.
6.
Translate the following into a standard-form categorical claim: It’s not only chemical-free
products that are organic.
Some organic products are not chemical-free products.
7.
Translate the following into a standard-form categorical claim: Not all savings institutions
are banks.
Some savings institutions are not banks.
8.
Translate the following into a standard-form categorical claim: Banks are the only savings
institutions.
All savings institutions are banks.
9.
Translate the following into a standard-form categorical claim: Banks are not the only
savings institutions.
Some savings institutions are not banks.
10.
Translate the following into a standard-form categorical claim: Only banks can be savings
institutions.
All savings institutions are banks.
11.
Translate the following into a standard-form categorical claim: People always leave when
Tony plays the accordion.
All times Tony plays the accordion are times people leave.
12.
Translate the following into a standard-form categorical claim: People always duck when
Richard picks up a golf club.
All times Richard picks up a golf club are times people duck.
13.
Translate the following into a standard-form categorical claim: Whenever Tony plays the
accordion, people leave.
All times Tony plays the accordion are times people leave.
14.
Translate the following into a standard-form categorical claim: People duck whenever
Richard picks up a golf club.
All times Richard picks up a golf club are times people duck.
15.
Translate the following into a standard-form categorical claim: Tricia’s dog goes wherever
she goes.
All places Tricia goes are places her dog goes.
16.
Translate the following into a standard-form categorical claim: Except for members of the
Lucero family, there’s nobody in the park.
All people in the park are members of the Lucero family.
17.
Translate the following into a standard-form categorical claim: There’s nobody in the park
except members of the Lucero family.
All people in the park are members of the Lucero family.
18.
Translate the following into a standard-form categorical claim: Lydia is the only person in
our group who sold stock before the crash.
All people in our group who sold stock before the crash are {people = Lydia} (that is,
people identical to Lydia).
19.
Translate the following into a standard-form categorical claim: The morning star is
actually the evening star.
All {things = the morning star} are {things = the evening star}.
20.
Translate the following into a standard-form categorical claim: Mr. Ashcroft isn’t at home.
No {people = Mr. Ashcroft} are people at home.
21.
Translate the following into a standard-form categorical claim: Only athletes play in the
National Basketball Association.
All who play in the National Basketball Association are athletes.
22.
Translate the following into a standard-form categorical claim: Not every gambler is a
criminal.
Some gamblers are not criminals.
23.
Translate the following into a standard-form categorical claim: Exceptional employees are
always rewarded.
All exceptional employees are recipients of rewards.
24.
Translate the following into a standard-form categorical claim: Few voters think critically.
Some voters are not critical thinkers.
25.
Translate the following into a standard-form categorical claim: Many Democrats are
conservative.
Some Democrats are conservatives.
26.
Translate the following into a standard-form categorical claim: Wherever there’s smoke,
there’s fire.
All places there is smoke are places there is fire.
27.
Translate the following into a standard-form categorical claim: Mechanics make great
lovers.
All mechanics are great lovers.
28.
Translate the following into a standard-form categorical claim: The only people who vote
are members.
All voters are members.
29.
Translate the following into a standard-form categorical claim: Angels aren’t real.
No real things are angels.
30.
Translate the following into a standard-form categorical claim: Richard Nixon was not
impeached.
No {people = Richard Nixon} are people who were impeached.
31.
Translate the following into a standard-form categorical claim: People can’t register
unless they pay the fee.
All people who can register are people who pay the fee.
32.
Translate the following into a standard-form categorical claim: There’s nobody here except
me.
All people who are here are {people = me}.
33.
Translate the following into a standard-form categorical claim: Nobody in middle school
did better on the exam than Lauren.
No students in middle school are people who did better on the exam than Lauren.
34.
Translate the following into a standard-form categorical claim: All the people I know who
are named “Brooke” have birthdays in December.
All people I know named “Brooke” are people with birthdays in December.
35.
Translate the following into a standard-form categorical claim: If it’s a gigantosaurus, then
it’s bigger than a tyrannosaurus rex.
All gigantosauruses are creatures that are bigger than a tyrannosaurus rex.
36.
Which of the following are similar claims?
a. If you haven’t been tested, then you cannot give blood.
b. If you can give blood, then you haven’t been tested.
c. You can give blood only if you’ve been tested.
d. Nobody who’s been tested cannot give blood.
e. Everybody who has not been tested cannot give blood.
Claims a, c, and e can all be translated as “All people who can give blood are people who
have been tested.” Claim d translates as “No people who have been tested are people who
can give blood,” while claim b translates as “People who can give blood are people who
have not been tested.”
37.
Using the square of opposition and the truth value of the first claim, determine the truth
values of the other claims.
a. True: All surprises are unpleasant events.
b. No surprises are unpleasant events.
c. Some surprises are unpleasant events.
d. Some surprises are not unpleasant events.
b: False; c: True; d: False.
38.
Using the square of opposition and the truth value of the first claim, determine the truth
values of the other claims.
a. True: Some winters are dry seasons.
b. No winters are dry seasons.
c. All winters are dry seasons.
d. Some winters are not dry seasons.
b: False; c: Undetermined; d: Undetermined.
39.
Using the square of opposition and the truth value of the first claim, determine the truth
values of the other claims.
a. False: No guppies are egg-layers.
b. All guppies are egg-layers.
c. Some guppies are egg-layers.
d. Some guppies are not egg-layers.
b: Undetermined; c: True; d: Undetermined.
40.
Using the square of opposition and the truth value of the first claim, determine what, if
anything, follows about the truth values of the other claims.
a. False: Some frozen dinners are nutritious meals.
b. All frozen dinners are nutritious meals.
c. No frozen dinners are nutritious meals.
d. Some frozen dinners are not nutritious meals.
b: False; c: True; d: True.
41.
Assume that the original claim is true, and follow the directions given. What is the truth
value of the claim you wind up with?
Some uninsured investments are risky deals.
(Convert this claim, then obvert the result.)
Some risky deals are not insured investments. (True)
42.
Assume that the original claim is true, and follow the directions given. What is the truth
value of the claim you wind up with?
All people who win lotteries are people who get lots of mail.
(Find the contrapositive, then convert.)
All people who do not win lotteries are people who do not get lots of mail. (Undetermined:
requires converting an A-claim)
43.
Assume that the original claim is true, and follow the directions given. What is the truth
value of the claim you wind up with?
No medical books are inexpensive books.
(Convert, then find the contradictory.)
Some inexpensive books are medical books. (False)
44.
Assume that the original claim is true, and follow the directions given. What is the truth
value of the claim you wind up with?
Some plutonium-contaminated soil storage areas in New Mexico are not areas that are
isolated from drinking-water supplies.
(Find the obverse, convert that, then find the subcontrary.)
Some areas that are not isolated from drinking-water supplies are plutonium-
contaminated soil storage areas in New Mexico. (Undetermined)
45.
Assume that the original claim is true, and follow the directions given. What is the truth
value of the claim you wind up with?
All non-isolated computer systems are systems that are at risk from computer viruses.
(Find the contrapositive, then find the contrary of the result.)
No systems that are not at risk from computer viruses are isolated computer systems.
(False)
46.
Assume that the original claim is true, and follow the directions given. What is the truth
value of the claim you wind up with?
No public television stations are stations that broadcast commercials.
(Obvert, then convert, and then find the contradictory.)
Some stations that do not broadcast commercials are not public television stations.
(Undetermined: cannot convert an A-claim)
47.
Assume that the original claim is true, and follow the directions given. What is the truth
value of the claim you wind up with?
All public television stations are stations that require underwriters.
(Contrapose, then find the contrary.)
No stations that do not require underwriters are nonpublic television stations. (False)
48.
Assume that the original claim is true, and follow the directions given. What is the truth
value of the claim you wind up with?
Some types of folk music are not examples of ethnic music.
(Obvert, then convert, then find the contradictory.)
No examples of nonethnic music are types of folk music. (False)
49.
Assume that the original claim is true, and follow the directions given. What is the truth
value of the claim you wind up with?
No people who made below C on the final are people who will make a good grade for the
course.
(Convert, then obvert, then find the contradictory.)
Some people who will make a good grade for the course are not people who did not make
below C on the final. (False)
50.
Assume that the original claim is true, and follow the directions given. What is the truth
value of the claim you wind up with?
All transmissions without lockups in the torque converters are transmissions that
overheat.
(Contrapose, then obvert, then find the contrary.)
All transmissions that fail to overheat are transmissions without lockups in the torque
converters. (False)
51.
Using the items in Exercise 9-12 in your text as examples, determine the truth value of the
second claim (below) based on that given for the first claim.
a. No Xs are non-Ys. (True)
b. Some Xs are Ys.
True.
52.
Using the items in Exercise 9-12 in your text as examples, determine the truth value of the
second claim (below) based on that given for the first claim.
a. All Xs are non-Ys. (True)
b. Some Ys are Xs.
53.
Using the items in Exercise 9-12 in your text as examples, determine the truth value of the
second claim (below) based on that given for the first claim.
a. Some non-Xs are not Ys. (False)
b. No Xs are non-Ys.
False.
54.
Using the items in Exercise 9-12 in your text as examples, determine the truth value of the
second claim (below) based on that given for the first claim. Translation into standard
form may be required.
a. Optical disks never wear out. (False)
b. Some disks other than optical disks do sometimes wear out.
Undetermined.
55.
Using the items in Exercise 9-12 in your text as examples, determine the truth value of the
second claim (below) based on that given for the first claim. Translation into standard
form may be required.
a. Some fish from the river have been found to contain toxic levels of trace minerals.
(True)
b. No fish in which toxic levels of trace minerals have not been found have come from the
river.
Undetermined.
56.
Using the items in Exercise 9-12 in your text as examples, determine the truth value of the
second claim (below) based on that given for the first claim. Translation into standard
form may be required.
a. Every editorial that Smathers has written has been one in which he attacks the city
council. (True)
b. At least one of the editorials that has not attacked the city council was not written by
Smathers.
True.
57.
Using the items in Exercise 9-12 in your text as examples, determine the truth value of the
second claim (below) based on that given for the first claim. Translation into standard
form may be required.
a. British comedies are always more sophisticated than American comedies. (False)
b. Some comedies that are no more sophisticated than American comedies come from
Britain.
True.
58.
Using the items in Exercise 9-12 in your text as examples, determine the truth value of the
second claim (below) based on that given for the first claim. Translation into standard
form may be required.
a. None of the clothes that were bought at Severn’s lasted very long. (True)
b. Some of the clothes that lasted a long time are clothes that were not bought at
Severn’s.
True.