# Social Science

Source: www.csus.edu/indiv/d/dowdenb/4/logical-reasoning.pdf

1. A deductive argument that is constructed in such a way that ** IF ** its premises are true, its conclusion

*must*be true is said to be…

Select one:

b. invalid.

c. strong.

d. probabilistic.

2. An inductive argument that is constructed in such a way that ** IF ** its premises are true, its conclusion is

*probably*true is said to be…

Select one:

a. strong.

b. valid.

c. invalid.

d. weak.

3. A deductively valid argument *that has true premises* is said to be…

Select one:

a. probable.

b. strong.

c. cogent.

d. sound.

4. An inductively strong argument *with true premises* is said to be…

Select one:

a. cogent.

b. sound.

c. valid.

d. invalid

**What follows with certainty from these three sentences? **

5. Only bears sleep in this house. Goldilocks is not a bear. Smokey is a bear.

Select one:

a. Smokey does not sleep in this house.

b. Smokey does sleep in this house.

c. Goldilocks does not sleep in this house.

d. none of the above

**6. Assess the quality of the following argument:**

Most wolves are not white. King is a wolf in the San Diego Zoo that we are going to visit tomorrow. So, he is not going to be white.

Select one:

a. inductively strong

b. deductively invalid

c. deductively valid

d. inductively very weak

**7. Is this argument deductively valid and sound?**

The current president of Russia is an Asian, and all Asians are dope addicts, so the president of Russia is a dope addict.

Select one:

a. no, it’s valid *but not sound*

b. no, it’s invalid

c. yes, it’s valid *and sound*

**8. This classic argument—**“All men are mortal. Socrates is a man. Therefore, Socrates is mortal”**—is…**

Select one:

a. inductively strong

b. deductively cogent

c. deductively invalid

d. deductively valid

**9. The argument—**“If he comes back, it’s probably because he wants money. There he is. He wants money”**—is…**

Select one:

a. strong

b. valid

c. invalid

d. complete

**10. The argument—**“If he comes back, it’s probably because he wants money. There he is. He wants money”**—is…**

Select one:

a. strong

b. valid

c. invalid

d. complete

USE THIS PASSAGE TO ANSWER THE FOLLOWING QUESTIONS:

[1] If you go to that party you’re completely nuts. [2] You’re going to the party. [3] It necessarily follows that you’re nuts.

11. Identify the conclusion in the passage above.

Select one:

a. Sentence [3]

b. Sentence [2]

c. Sentence [1]

12. Determine whether the above passage is meant to be deductive or inductive.

Select one:

a. Inductive

b. Deductive

13. Determine whether above passage is valid, invalid, strong, or weak.

Select one:

a. strong

b. valid

c. weak

d. invalid

14.** Indicate whether the following argument is best characterized as valid or invalid, strong or weak:**

“Any sitcom that tried to imitate *Seinfeld *is probably a piece of trash. All of this season’s sitcoms try to ape *Seinfeld. *They’ve gotta be trash.”

Select one:

a. weak

b. valid

c. invalid

d. strong

**15. Indicate whether the following argument is best characterized as valid or invalid, strong or weak:**

“If you’re eighteen, you’re eligible to vote. But you’re only seventeen. You’re not eligible to vote.”

[[ *NOTE*: it might help to treat “seventeen” as “not eighteen” ]]

Select one:

a. valid

b. invalid

c. strong

d. weak

**16. Determine whether the following argument is valid or invalid.**

If the butler didn’t kill the master, then the maid did. The butler didn’t kill him. So, the maid killed him.

Select one:

a. valid

b. invalid

**17. Determine whether the following argument is valid or invalid:**

If laws could stop crime, there would be no crime. But there is crime. Therefore, laws cannot stop crime.

[[ NOTE: *be wary of your intuitions* … it might help to notice that “there is crime” corresponds to “it is not the case that there is no crime” ]]

Select one:

a. invalid

b. valid

** 18. Modus ponens ** has this argument pattern…

Select one:

a. Either *p* or *q*. Not *p*. Therefore, *q*.

b. If *p*, then *q*. If *q*, then *r*. Therefore, if *p*, then *r*.

c. If *p*, then *q*. *p*. Therefore, *q*.

d. If p, then q. q. Therefore, p.

19. The invalid argument form known as ** affirming the consequent **has this pattern:

Select one:

a. If *p*, then *q*. *p*. Therefore, *q*.

b. If *p*, then *q*. *q*. Therefore, *p*.

c. If *p*, then *q*. Not *p*. Therefore, not *q*.

d. Either *p* or *q*. Not *p*. Therefore, *q*.

20. The invalid argument form known as ** denying the antecedent ** has this pattern:

Select one:

a. If *p*, then *q*. *p*. Therefore, *q*.

b. If *p*, then *q*. If *q*, then *r*. Therefore, if *p*, then *r*.

c. If *p*, then *q*. Not *p*. Therefore, not *q*.

d. If *p*, then *q*. *q*. Therefore, *p*.

21.** This argument—**“If Buffalo is the capital of New York, then Buffalo is in New York. Buffalo is in New York. Therefore, Buffalo is the capital of New York”**—is an example of…**

Select one:

a. affirming the consequent.

b. modus ponens

c. disjunctive syllogism.

d. denying the antecedent.

22.** This argument—**“If Einstein invented the steam engine, then he’s a great scientist. Einstein did not invent the steam engine. Therefore, he is not a great scientist”**—is an example of…**

Select one:

a. modus ponens

b. denying the antecedent.

c. affirming the consequent.

d. modus Tollens

**Indicate which of the following symbolized statements are true and which are false.**

*Assume that the variables a, b, c are TRUE*

*Assume that the variables p, q, r are FALSE*

23. a & p

Select one:

a. False

b. True

24. b v r

Select one:

a. False

b. True

25. c → q

Select one:

a. False

b. True

26. b v ~p

Select one:

a. False

b. True

27. a & c

Select one:

a. True

b. False

28.b → ~c

Select one:

a. True

b. False

**29. A conditional is false only when the antecedent is…**

Select one:

a. true and the *consequent *is false

b. false and the *consequent *is false

c. true and the *consequent *is true

d. false and the *consequent *is true

**30. The truth-table test of validity is based on the fact that it is impossible for a valid argument to have true premises and…**

Select one:

a. a *negated conclusion*

b. a *conditional*

c. a *false conclusion*

d. a *true conclusion*

**31. The name of the following argument form is…**

Select one:

a. disjunctive syllogism

b. denying the consequent

c. *modus tollens*

d. denying the antecedent

32.** Describe the logical form of the main argument below:**

Assuming x = 4 and y < 7, as you have said, then x is *not unequal to* 4

**Let…**

P is x=4

Q is y<7

Select one:

a.

P P or Q

b.

P If not-Q, then not-P Q

c. not-P If P, then Q ~P

d. P and Q not-not-P

**33. State whether the argument below (the same as the previous question) is a deductively valid inference:**

Assuming x = 4 and y < 7, as you have said, then x is *not unequal to* 4

Select one:

a. Yes, it is a deductively valid inference

b. No, it is not a deductively valid inference

**34. Is the argument in the following passage deductively valid? **

Your information establishes that President Abraham Lincoln was assassinated by Ulysses Grant. Now we can be sure that John was right when he said, “Abraham Lincoln was assassinated by Grant or Booth.”

[[ *NOTE*: be careful to correctly distinguish between the conclusion and the premise/s. ]]

Select one:

a. No, it is not deductively valid

b. Yes, it is deductively valid

**35. Which passage commits the fallacy of denying the antecedent? **

Select one:

a. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. The average citizen of Tokyo in 1890 did not eat pork regularly. So pork prices did not continue to drop in Japan from 1789 to 1889.

b. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. Pork prices continued to drop in Japan during that time. Consequently, the average citizen of Tokyo in 1890 did eat pork regularly.

c. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. The average citizen of Tokyo in 1890 did eat pork regularly. So pork prices did continue to drop in Japan from 1789 to 1889.

d. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. The average citizen of Tokyo in 1890 did not eat pork regularly. So pork prices did continue to drop in Japan from 1789 to 1889.

e. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. So the average citizen of Tokyo in 1890 did not eat pork regularly, because pork prices did not continue to drop in Japan from 1789 to 1889.

**36. Which passage commits the fallacy of affirming the consequent? **

Select one:

a. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. The average citizen of Tokyo in 1890 did not eat pork regularly. So pork prices did not continue to drop in Japan from 1789 to 1889.

b. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. Pork prices continued to drop in Japan during that time. Consequently, the average citizen of Tokyo in 1890 did eat pork regularly.

c. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. The average citizen of Tokyo in 1890 did eat pork regularly. So pork prices did continue to drop in Japan from 1789 to 1889.

d. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. The average citizen of Tokyo in 1890 did not eat pork regularly. So pork prices did continue to drop in Japan from 1789 to 1889.

e. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. So the average citizen of Tokyo in 1890 did not eat pork regularly, because pork prices did not continue to drop in Japan from 1789 to 1889.

**37. Which passage is an example of modus ponens? **

Select one:

a. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. The average citizen of Tokyo in 1890 did eat pork regularly. So pork prices did continue to drop in Japan from 1789 to 1889.

b. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. Pork prices continued to drop in Japan during that time. Consequently, the average citizen of Tokyo in 1890 did eat pork regularly.

c. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. The average citizen of Tokyo in 1890 did not eat pork regularly. So pork prices did not continue to drop in Japan from 1789 to 1889.

d. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. So the average citizen of Tokyo in 1890 did not eat pork regularly, because pork prices did not continue to drop in Japan from 1789 to 1889.

e. If pork prices continued to drop in Japan from 1789 to 1889, then pork would have been eaten regularly by the average citizen of Tokyo in 1890. The average citizen of Tokyo in 1890 did not eat pork regularly. So pork prices did continue to drop in Japan from 1789 to 1889.

**38. Are all three of these sentences logically equivalent to each other? If not, which two are equivalent to each other? **

1. If you’re from California, then you’re from San Francisco.

2. You’re from California if you’re from San Francisco.

3. You’re from San Francisco if you’re from California.

Select one:

a. sentences 1 and 3 are logically equivalent to each other

b. sentences 1 and 2 are logically equivalent to each other

c. none of the sentences are logically equivalent to each other

d. sentences 2 and 3 are logically equivalent to each other

e. all three are equivalent to each other

39. Which of the following sentences is a ** tautology **?

[[ *NOTE*: It would be helpful to use a truth table to work through this exercise ]]

Select one:

a. P & (~P v Q)

b. ~Q & (P & (P → Q))

c. (P → Q) v ~(P → Q)

d. none of the above

40. Which of the following sentences is a ** contradiction **?

[[ *NOTE*: It would be helpful to use a truth table to work through this exercise ]]

Select one:

a. P & (~P v Q)

b. ~Q & (P & (P → Q))

c. (P → Q) v ~(P → Q)

d. none of the above

41. Which of the following sentences is ** contingent **?

[[ *NOTE*: It would be helpful to use a truth table to work through this exercise ]]

Select one:

a. P & (~P v Q)

b. ~Q & (P & (P → Q))

c. (P → Q) v ~(P → Q)

d. none of the above

**42. The sentence Q v ~P is equivalent to one and only one of the following sentences. Which one?**

[[ *NOTE*: if you cannot spot the answer right away, it might be helpful to use truth tables to discover it ]]

Select one:

a. P → Q

b. ~P → ~Q

c. ~P → Q

d. Q → P

e. P → ~Q

43.** Is the following a deductively valid argument?**

If P, then Q

P

P and Q

Select one:

a. no, it is deductively invalid

b. yes, it is deductively valid

44.** Is the following a deductively valid argument?**

Q or not-Q

If P, then Q

not-P

not-Q

Select one:

a. no, it is deductively invalid

b. yes, it is deductively valid

**45. Is the following a deductively valid argument?**

P v ~P

P→Q

Q v ~Q

Select one:

a. yes, it is deductively valid

b. no, it is deductively invalid

**46. Is this argument deductively valid? Defend your answer by appeal to sentential logic.**

If Einstein were alive today, the physics department at Princeton University in New Jersey would be affected by his presence. So, if you look at the department you’ll see he’s one dead duck.

[[ *Note*: there is an implicit premise here ]]

Select one:

a. the argument is in the invalid form “*denying the antecedent*”

b. the argument is in the valid form “*modus ponens*”

c. the argument is in the invalid form “*affirming the consequent*”

d. the argument is in the valid form “*modus tollens*”

**47. Complete the following sentence:**

You can usually get from the bottom floor to the top floor of a building that has an elevator _________ you walk up the stairs.

Select one:

a. only if

b. if and only if

c. none of the above

d. unless

48.** Complete the following sentence:**

You are president of the United States _______________ you are a U.S. citizen.

Select one:

a. only if

b. if and only if

c. none of the above

d. unless

49.** Complete the following sentence:**

You are president of the United States ________________ you are ** not ** president of the United States.

Select one:

a. if and only if

b. none of the above

c. unless

d. only if

50.** Indicate whether the following is a deductively valid argument:**

Joseph will not graduate in cosmetology ** unless **he passes either the developmental cosmetology course or the course in experimental design. So, if Joseph passes experimental design, he will graduate in cosmetology.

Select one:

a. no, it is deductively invalid

b. yes, it is deductively valid

51. Are these two arguments** logically analogous **?

1. Carlucci will call us only if the war room is in condition orange, but the war room is in condition orange. So Carlucci will call.

2. Carlucci will call us only if he is alive. Carlucci is alive, so he will call.

Select one:

a. no, they are *not *logically analogous

b. yes, they are logically analogous

52. Are these two sentence forms ** logically equivalent **? (i.e. Do these two sentences logically imply each other regardless of their truth value?)

1. Not all fish in the Indian Ocean are land dwellers.

2. Some fish in the Indian Ocean are not creatures that live on land.

Select one:

a. yes, they are logically equivalent

b. no, they are *not *logically equivalent

53.** Use the space provided to create a truth table for this argument: **

P & (Q v ~P)

~Q→P

Q

**Make sure you construct the truth table according to how our book dictates. Type it all out and keep it neat in order to demonstrate your comprehension of this tool. The table I provide might have more columns than you need. Partial credit will be provided.**

**After you construct your truth table, indicate whether the argument is valid or invalid.**

** Valid or Invalid **?

54.** Use the space provided to create a truth table for this argument: **

B & (~C → ~B)

~C

**Make sure you construct the truth table according to how our book dictates. Type it all out and keep it neat in order to demonstrate your comprehension of this tool. The table I provide might have more columns than you need. Partial credit will be provided.**

**After you construct your truth table, indicate whether the argument is valid or invalid.**

** Valid or Invalid **?