Question 1

Determine whether the argument is valid or invalid.
-Michael Bolton is a hunk or Madonna cannot sing. If Madonna cannot sing, then Cigar does not win the Triple Crown. Cigar wins the Triple Crown. Therefore, Michael Bolton is not a hunk.
A)Valid
B)Invalid

Accepted Answer

The argument is invalid because it commits the fallacy of denying the antecedent. The fact that Cigar wins the Triple Crown only negates the consequent (Madonna cannot sing), not the entire conditional statement, leaving the possibility that Michael Bolton is a hunk unaffected.

Question 2

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-No cars come from Iceland.
A)If it doesn't come from Iceland, then it is not a car.
B)If it's not a car, then it comes from Iceland.
C)No cars come from Iceland.
D)If it is a car, then it doesn't come from Iceland.

Accepted Answer

The correct logical equivalent using the if...then connective is "If it is a car, then it doesn't come from Iceland," which directly translates the original statement into a conditional format.

Question 3

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-If I get robbed, I will go to court. I got robbed.
A)I will go to court.
B)I will not go to court.
C)I will not get robbed in court.
D)I will get robbed in court.

Accepted Answer

Let R represent "I get robbed" and C represent "I go to court."
Premise 1: R → C
Premise 2: R
Conclusion: C

This is a valid argument because the premises lead directly to the conclusion. If "I get robbed" (R) is true, then according to the first premise I must "go to court" (C). And since the second premise states that "I got robbed" is true, we can conclude without a doubt that "I will go to court."

Question 4

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime.
A)Squirrels do not scurry during the day.
B)The squirrels are not scurrying.
C)The squirrels are scurrying.
D)Squirrels do not scurry at night.

Accepted Answer

Given the premises: 1) It is either day or night. 2) If it is daytime, then the squirrels are scurrying. 3) It is not nighttime. From these, we can conclude that it is daytime, and therefore, according to premise 2, the squirrels are scurrying.

Question 5

Determine whether the argument is valid or invalid.
-If Cathy is a gambler, then she lives in Marine. Cathy lives in Marine and she loves horses. Therefore, if Cathy does not love horses, she is not a gambler.
A)Valid
B)Invalid

Accepted Answer

The argument is valid because it follows the contrapositive rule. If "If P then Q" is true, then "If not Q then not P" is also true. Here, P is "Cathy is a gambler" and Q is "she lives in Marine." The conclusion correctly applies this logic.

Question 6

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-All birds have wings. None of my pets are birds. All animals with wings can flap them.
A)None of my pets can flap their wings.
B)No birds can flap their wings.
C)All my pets can flap their wings.
D)All birds can flap their wings.

Accepted Answer

The answer of Use the method of writing each premise...

Question 7

Determine whether the argument is valid or invalid.
-The Rams will be in the playoffs if and only if Ozzie is an all-star. Mark loves the Rams or Ozzie is an all-star. Mark does not love the Rams. Therefore, the Rams will not be in the playoffs.
A)Valid
B)Invalid

Accepted Answer

The answer of Determine whether the argument is valid or...

Question 8

Determine whether the argument is valid or invalid.
-If I hear that poem, it reminds me of my mother. If I get sentimental, then it does not remind me of my mother. I get sentimental. Therefore, I don't hear that poem.
A)Valid
B)Invalid

Accepted Answer

The argument is valid. The premises lead logically to the conclusion. If hearing the poem reminds the speaker of their mother, and getting sentimental means it does not remind them of their mother, then if they are sentimental, they cannot be hearing the poem.

Question 9

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-I have not accepted anyone who is from out of town.
A)If I have not accepted a person, then they are from out of town.
B)If the person is from out of town, I have not accepted them
C)If the person is not from out of town, I have accepted them
D)If I have accepted a person, then they are from out of town.

Accepted Answer

The original statement implies that being from out of town is a condition that leads to not being accepted. Therefore, the correct restatement using the if...then connective is option B, which directly translates the original condition and its consequence.

Question 10

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-Cats chase mice.
A)Cats chase mice.
B)If it is a cat, then it chases mice.
C)If a cat is chasing it, then it is a mouse.
D)If cats chase, then they chase mice.

Accepted Answer

The correct logical form using the if...then connective that captures the essence of the statement "Cats chase mice" is "If it is a cat, then it chases mice." This form clearly establishes the condition (being a cat) and the consequence (chasing mice).

Question 11

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-A ship can't sail on land.
A)If this is a ship, then it can't sail on land.
B)If this is not land, then a ship can't sail.
C)If this is a ship, then it can sail on land.
D)A ship can't sail on land.

Accepted Answer

The original statement implies that the condition of being a ship excludes the possibility of sailing on land, which is correctly reformulated in option A using the if...then structure.

Question 12

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-All children like stuffed toys.
A)If children like it, then it's a stuffed toy.
B)If it is not a stuffed toy, then children like it.
C)If it is a child, then it likes stuffed toys.
D)All children like stuffed toys.

Accepted Answer

The original statement "All children like stuffed toys" is best rewritten in the if...then format as "If it is a child, then it likes stuffed toys," which directly translates the universal claim about children's preferences into a conditional statement.

Question 13

Determine whether the argument is valid or invalid.
-If I were your friend and you were my soul mate, then I'd never stop liking you. I've stopped liking you. Therefore, I am not your friend or you were not my soul mate.
A)Valid
B)Invalid

Accepted Answer

The argument is valid due to the contrapositive rule in logic. If the original statement is "If P, then Q," the contrapositive is "If not Q, then not P," which logically has the same truth value as the original statement. Here, "I've stopped liking you" negates the consequent of the original conditional statement, leading to the conclusion that the antecedent ("If I were your friend and you were my soul mate") is not true, either in whole or in part.

Question 14

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-No turkeys like Thanksgiving.
A)If it is a turkey, then it doesn't like Thanksgiving.
B)If it is not a turkey, then it likes Thanksgiving.
C)If it is Thanksgiving, then turkeys like it.
D)If it is not Thanksgiving, then no turkeys like it.

Accepted Answer

The original statement "No turkeys like Thanksgiving" directly translates to "If it is a turkey, then it doesn't like Thanksgiving," indicating a conditional relationship where being a turkey implies a dislike for Thanksgiving.

Question 15

Determine whether the argument is valid or invalid.
-If Ann so wishes, then Bill will be the president. Manuel is a public defender or Bill will be the president. Manuel is not a public defender. Therefore, Ann does not so wish.
A)Valid
B)Invalid

Accepted Answer

The argument is invalid because it commits a logical fallacy. Even if Manuel is not a public defender and Bill will be the president, it does not logically follow that Ann does not wish for Bill to be the president. The premises do not necessarily lead to the conclusion.

Question 16

Determine whether the argument is valid or invalid.
-All women are wealthy. Amanda is a woman. Therefore, Amanda is wealthy.
A)Valid
B)Invalid

Accepted Answer

The argument is valid because it follows a logical structure: if all women are wealthy and Amanda is a woman, then it logically follows that Amanda is wealthy. This does not assess the truth of the premises, only the logical structure.

Question 17

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-I'll leave when he arrives.
A)If I leave, then he will leave.
B)If I will leave, then he'll arrive.
C)I'll leave when he arrives.
D)If he arrives, then I'll leave.

Accepted Answer

The correct logical structure for "I'll leave when he arrives" using the if...then connective is "If he arrives, then I'll leave," which matches option D.

Question 18

Determine whether the argument is valid or invalid.
-Sam plays tennis or George is not a man. If George is not a man, then Betsy does not win the award. Betsy wins the award. Therefore, Sam does not play tennis.
A)Valid
B)Invalid

Accepted Answer

The argument is invalid because the conclusion "Sam does not play tennis" does not logically follow from the premises. The premises do not provide a definitive link between Betsy winning the award and Sam playing tennis.

Question 19

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-All chocolate is good.
A)If it isn't chocolate, then it isn't good.
B)Chocolate is good.
C)If it's good, then it's got to be chocolate.
D)If it's chocolate, then it's good.

Accepted Answer

The original statement "All chocolate is good" directly translates to the conditional statement "If it's chocolate, then it's good," which matches option D. This is because the original statement implies a condition (being chocolate) and a result (being good), which is the structure of an if...then statement.

Question 20

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-Every man with a mind can think. A distracted man can't think. A man who is not distracted can apply himself.
A)Every man with a mind is distracted.
B)Every distracted man can apply himself.
C)Every man with a mind can apply himself.
D)Every man who can apply himself has a mind.

Accepted Answer

The premises suggest that having a mind enables thinking, being distracted inhibits thinking, and not being distracted allows for application of oneself. Since every man with a mind can think, and the ability to apply oneself is contingent on not being distracted (which implies the ability to think), it logically follows that every man with a mind (who can think and is not distracted) can apply himself.

Quiz 3: Introduction to Logic

Determine whether the argument is valid or invalid. -Michael Bolton is a hunk or Madonna cannot sing. If Madonna cannot sing, then Cigar does not win the Triple Crown. Cigar wins the Triple Crown. Therefore, Michael Bolton is not a hunk.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -No cars come from Iceland.

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -If I get robbed, I will go to court. I got robbed.

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime.

Determine whether the argument is valid or invalid. -If Cathy is a gambler, then she lives in Marine. Cathy lives in Marine and she loves horses. Therefore, if Cathy does not love horses, she is not a gambler.

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -All birds have wings. None of my pets are birds. All animals with wings can flap them.

Determine whether the argument is valid or invalid. -The Rams will be in the playoffs if and only if Ozzie is an all-star. Mark loves the Rams or Ozzie is an all-star. Mark does not love the Rams. Therefore, the Rams will not be in the playoffs.

Determine whether the argument is valid or invalid. -If I hear that poem, it reminds me of my mother. If I get sentimental, then it does not remind me of my mother. I get sentimental. Therefore, I don't hear that poem.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -I have not accepted anyone who is from out of town.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -Cats chase mice.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -A ship can't sail on land.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -All children like stuffed toys.

Determine whether the argument is valid or invalid. -If I were your friend and you were my soul mate, then I'd never stop liking you. I've stopped liking you. Therefore, I am not your friend or you were not my soul mate.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -No turkeys like Thanksgiving.

Determine whether the argument is valid or invalid. -If Ann so wishes, then Bill will be the president. Manuel is a public defender or Bill will be the president. Manuel is not a public defender. Therefore, Ann does not so wish.

Determine whether the argument is valid or invalid. -All women are wealthy. Amanda is a woman. Therefore, Amanda is wealthy.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -I'll leave when he arrives.

Determine whether the argument is valid or invalid. -Sam plays tennis or George is not a man. If George is not a man, then Betsy does not win the award. Betsy wins the award. Therefore, Sam does not play tennis.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -All chocolate is good.

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -Every man with a mind can think. A distracted man can't think. A man who is not distracted can apply himself.