Question 1

Let $$p$$ represent the statement "One plays hard." What is the symbolic form for "One does not play hard"?

Accepted Answer

$$\sim p$$

Question 2

Given $$p$$: "The Pilgrims did not land in Tahiti." What is the negation of $$p in $$words?

Accepted Answer

The Pilgrims landed in Tahiti.

Question 3

Express the quantified statement "No politicians have told a lie" in an equivalent way.

Accepted Answer

All politicians have not told a lie.

Question 4

Write the negation of the quantified statement: "All mathematicians are humans."

Accepted Answer

Some mathematicians are not humans.

Question 5

Given $$p$$: "1984 is a novel." and $$q$$: "Persuasion is a novel." What is the symbolic form for "1984 is a novel and Persuasion is a novel"?

Accepted Answer

$$p \land q$$

Question 6

Given $$p$$: "The car has been repaired." $$q$$: "The kids are home." $$r$$: "We will visit Aunt Tillie." What does $$(p \land q) \rightarrow r$$ mean in words?

Accepted Answer

If the car has been repaired and the kids are home, we will visit Aunt Tillie.

Question 7

Let $$p$$: "I like the song." $$q$$: "The DJ is entertaining." $$r$$: "I change the station." What is the symbolic form for "I change the station if and only if it's not true that both I like the song and the DJ is entertaining"?

Accepted Answer

$$r \leftrightarrow \sim(p \land q)$$

Question 8

Use De Morgan's laws to write the negation of "Cats are lazy or dogs aren't friendly."

Accepted Answer

Cats aren't lazy and dogs are friendly.

Question 9

Given the argument: "All dogs like food. All pets like food. Therefore, all dogs are pets." Is this argument valid or invalid according to an Euler diagram?

Accepted Answer

Invalid

Question 10

Translate the argument: "We will lower the drinking age or we will require three photo IDs. We will not require three photo IDs. Therefore, we will lower the drinking age." Which type of reasoning is used and is the argument valid?

Accepted Answer

Disjunctive reasoning; valid

Question 11

Given $$p is $$true and $$q is $$false, what is the truth value of $$[(\sim p \lor \sim q) \land \sim q]$$?

Accepted Answer

True

Question 12

Write the contrapositive of the statement: "If the electricity is out, then I cannot use the computer."

Accepted Answer

If I can use the computer, then the electricity is not out.

Question 13

Write the negation of the conditional statement: "If there is a flood, then all policemen are on call."

Accepted Answer

There is a flood and some policemen are not on call.

Question 14

Given the symbolic statement $$\sim(p \lor q)$$, which row in the truth table will result in a true value for $$\sim(p \lor q)$$?

Accepted Answer

When $$p is $$false and $$q is $$false

Question 15

Construct a truth table for $$\sim(p \rightarrow \sim q). $$Which row(s) will result in a true value for $$\sim(p \rightarrow \sim q)$$?

Accepted Answer

When $$p is $$true and $$q is $$false

Question 16

Which of the following is the converse of the statement: "If you are running on the beach, then you are not dancing."

Accepted Answer

If you are not dancing, then you are running on the beach.

Question 17

Which of the following is the inverse of the statement: "If you are running on the beach, then you are not dancing."

Accepted Answer

If you are not running on the beach, then you are dancing.

Question 18

Given the argument: $$p \rightarrow q$$, $$\sim p$$, therefore $$\sim q. Is $$this argument valid or invalid?

Accepted Answer

Invalid

Question 19

Which logical fallacy is committed in the argument: $$p \rightarrow q$$, $$q$$, therefore $$p$$?

Accepted Answer

Fallacy of the converse

Logic, Symbolic Statements, and Validity: Liberal Arts Math Chapter 3 Review Guidance

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