Deck 7: Evaluating Truth-Functional Arguments

Question 1

Identify the argument form for each of the following symbolized arguments

- $\begin{array}{l}\mathrm{A} \supset(\mathrm{B} \vee \mathrm{C}) \\ \sim\underline{ \mathrm{B} \cdot \sim \mathrm{C}} \\ \therefore \sim \mathrm{A}\end{array}$

A) modus ponens
B) modus tollens
C) denying the antecedent
D) affirming the consequent

Answer 1

modus tollens

Question 2

Choose the correct translation for each of the following compound claims.

-Small scale agriculture will be profitable and growers will get subsidies, only if demand for local food does not decrease.

A) ~ [D $\sqsupset$ (P • S)]
B) (P • S) $\sqsupset$ ~ D
C) ~ D $\sqsupset$ (P • S)
D) P • (S $\sqsupset$ ~ D)

Answer 2

(P • S) $\sqsupset$ ~ D

Question 3

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by identifying the argument form.

-The death penalty will deter terrorists only if it deters murderers. Consequently, the death penalty will not deter terrorists since it has been shown to not deter murderers.

Answer 3

$\begin{array}{l}\mathrm{T} \supset \mathrm{M} \\ \sim \underline{\mathrm{M}} \\ \therefore \sim \mathrm{T}\end{array}$
modus tollens; valid

Question 4

Choose the correct translation for each of the following compound claims.

-It is not the case that Ese speaks Urdu and French.

A) ~ U • ~ F
B) ~ (U • F)
C) ~ (U $\lor$ F)
D) ~ U • F

Question 5

Choose the correct translation for each of the following compound claims.

-If you are eligible for swimming, then you are eligible for water polo.

A) S $\lor$ W
B) W $\sqsupset$ S
C) S $\sqsupset$ W
D) S • W

Question 6

Identify the argument form for each of the following symbolized arguments

- $\begin{array}{l}\mathrm{A} \supset(\mathrm{B} \cdot \mathrm{C}) \\ \underline{B \cdot C} \\ \therefore \mathrm{A}\end{array}$

A) modus ponens
B) modus tollens
C) denying the antecedent
D) affirming the consequent

Question 7

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by identifying the argument form.

-Susan is not going swimming. This is because if Susan goes swimming, then the tide must be going out, and the tide is not going out.

Question 8

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by identifying the argument form.

-Your health insurance isn't good. Given that you won't receive good health care unless you have good health care insurance, that means that you will not get good health care.

Question 9

Choose the correct translation for each of the following compound claims.

-This spring, Michael will go to Europe or travel through China, and he will keep a daily journal.

A) E $\lor$ C • J
B) (E $\lor$ C) • J
C) E $\lor$ (C • J)
D) (E • C) $\lor$ J

Question 10

Choose the correct translation for each of the following compound claims.

-Either kestrels winter in Mexico and summer in Canada, or they remain all year here in Alabama.

A) (M • C) $\lor$ A
B) (M $\lor$ C) • A
C) M • C $\lor$ A
D) M • (C $\lor$ A)

Question 11

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by identifying the argument form.

-If managers plan to give themselves a raise, then they will either raise the pay of the analysts or they will ask for more money from investors. Therefore, since they neither raised the pay of the analysts nor asked for more money from investors, managers must not be planning to give themselves a raise.

Question 12

Choose the correct translation for each of the following compound claims.

-You can enter the chess tournament only if you are ranked.

A) R $\lor$ C
B) C $\lor$ R
C) C $\sqsupset$ R
D) R $\sqsupset$ C

Question 13

Choose the correct translation for each of the following compound claims.

-You cannot enter the chess tournament unless you are ranked.

A) R • ~ C
B) C $\lor$ R
C) ~ C $\sqsupset$ R
D) ~ R $\sqsupset$ ~ C

Question 14

Identify the argument form for each of the following symbolized arguments

- $\begin{array}{l}(\mathrm{A} \cdot \mathrm{B}) \supset \mathrm{C} \\ \sim \underline{\mathrm{A} \vee \sim \mathrm{B}} \\ \therefore \mathrm{C}\end{array}$

A) modus ponens
B) modus tollens
C) denying the antecedent
D) affirming the consequent

Question 15

Choose the correct translation for each of the following compound claims.

-You can enter the chess tournament if you are ranked.

A) R $\lor$ C
B) C $\lor$ R
C) C $\sqsupset$ R
D) R $\sqsupset$ C

Question 16

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by identifying the argument form.

-Peter Singer argues that meat consumption is unethical, and he's right. This is because meat consumption is ethical only if animals are treated humanely, and our current food industry does not treat animals humanely.

Question 17

Choose the correct translation for each of the following compound claims.

-Neither a sculpture nor a painting will be exhibited in the new gallery.

A) S • P
B) ~ (S • P)
C) ~ S $\lor$ ~ P
D) ~ (S $\lor$ P)

Question 18

Identify the argument form for each of the following symbolized arguments

- $\begin{array}{l}(\mathrm{A} \cdot \mathrm{B}) \supset \mathrm{C} \\ \sim \underline{\mathrm{A} \vee \sim \mathrm{B}} \\ \therefore \mathrm{C}\end{array}$

A) modus ponens
B) modus tollens
C) denying the antecedent
D) affirming the consequent

Question 19

Choose the correct translation for each of the following compound claims.

-Phyllis will be late for the exam if she swims with the team and lifts weights with her friend.

A) (S • W) $\sqsupset$ E
B) E $\sqsupset$ (S • W)
C) S • (W $\sqsupset$ E)
D) (E $\sqsupset$ S) • W

Question 20

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by identifying the argument form.

-The war on drugs will succeed in the 1990's if Prohibition succeeded in the 1920's. But Prohibition did not succeed in the 1920's. So, the war on drugs will not succeed in the 1990's.

Question 21

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by using the Shortcut Method.

-Can you believe what is now going on in the art world? If either the art historians are not correct or the artists are not progressive, then retro art is not just a fad. Therefore, neither the art historians or the critics are correct, since Dada is boring and retro art is just a fad.

Question 22

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by using the Shortcut Method.

-Charles is not cheating and Vincent is deceptive, only if Hank is not aggressive. Now, if Bradley is trustworthy, then Charles is not cheating. Thus, since either Hank is aggressive or Charles is cheating, it's not the case that both Hank is aggressive and Bradley is trustworthy.

Question 23

How can you accuse the police chief of bias since he has never treated someone unfairly?

Question 24

Determine whether the argument is valid or invalid by using the Shortcut Method

- $\begin{array}{l}\mathrm{Q} \vee \sim \mathrm{E} \\\underline{ \sim \mathrm{Q}} \\ \therefore \sim \mathrm{E}\end{array}$

Question 25

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by using the Truth Table Method.

-Since we planned to go to either Egypt or Thailand this summer, it's clear that we will be traveling to Thailand. Isn't it still dangerous to travel to Egypt right now?

Question 26

Write a Complete Analysis plus Evaluation for each of the following passages.

-Psychologists at the University of Manitoba performed an experiment in which high school students who exercised before school did better in their early morning math class. The exercise was most likely the cause of the improvement in math, given that of the three groups of students in the study, only the students who exercised before math class showed improvement.

Question 27

Determine whether the argument is valid or invalid by using the Truth Table Method.

- $\begin{array}{l}A \cdot B \\ \sim \underline{B} \\ \therefore \sim A\end{array}$

Question 28

If superstring theory is proven correct, we will be forced to accept that the reality we have known is but a delicate chiffon draped over a thick and richly textured cosmic fabric. -Brian Greene, The Fabric of the Cosmos

Question 29

Write a Complete Analysis plus Evaluation for each of the following passages.

-Either wealth is an evil or wealth is a good; but wealth is not an evil; therefore wealth is a good. - Sextus Empiricus, Against the Logicians

Question 30

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by using the Truth Table Method.

-If you are not married and have an infant, then you are sleep deprived. Therefore, you must get plenty of sleep since you are neither unmarried nor have an infant.

Question 31

Determine whether the argument is valid or invalid by using the Shortcut Method

-P $\sqsupset$ S
J $\sqsupset$ S
$\therefore$ P $\sqsupset$ J

Question 32

Determine whether the argument is valid or invalid by using the Truth Table Method.

- $\begin{array}{l}A \vee(B \supset C) \\ \frac{B \cdot C}{\therefore A}\end{array}$

Question 33

Write a Complete Analysis plus Evaluation for each of the following passages.

-If the government does not do something about white-collar crime, then we will not have a rebound in the stock market. Since the government will certainly be doing something about white-collar crime because Congress demands action, we can count on seeing the stock market rebound.

Question 34

If Egypt's elected leader is not both dictatorial and intolerant, then he is not obstructing democratic reforms. Due to the fact that he is not obstructing democratic reforms, Egypt's elected leader is not dictatorial.

Question 35

Translate each of the following arguments into symbolic form. Then, determine whether the argument is valid or invalid by using the Truth Table Method.

-Either Lady Gaga will win the award for Best Female Pop Vocal Performance or she will win Best New Artist. And she will win Best Female Pop Vocal Performance if she wins Best New Artist. Therefore, Lady Gaga will win both awards.