Homework 2

Complete the following truth table for​ 'if p, then​ q.'

p q if p, then q T T T T F F F T T F F T

Make a truth table for each of the following statements. Explain all the truth values in the table. p and​ q; p or​ q; if​ p, then q

p q p and q T T T T F F F T F F F F

Complete the following truth table for​ 'p or​ q.'

p q p or q T T T T F T F T T F F F

Give an example of an inclusive or. Choose the correct answer below.

A quadrilateral can be a polygon with 4 sides or a polygon with 4 vertices.

Give an example of an exclusive or. Choose the correct answer below.

Before the​ test, I have the choice of studying or watching television.

Which of the following has the form of a conditional​ statement? Explain your reasoning.

The phrase​ 'if x, then​ y' has the form of a conditional statement because conditional statements use the words​ "if" and​ "then."

Explain when​ 'if p, then​ q' is true. Select all that apply.

if p, then​ q' is true when p is false and q is true. ​'if p, then​ q' is true when both p and q are true. ​'if p, then​ q' is true when both p and q are false.

Define​ conjunction, disjunction, and​ conditional, and give an example of each in words.

Given two propositions p and​ q, the statement p and q is called their conjunction. It is true only if p and q are both true.

Define disjunction. Choose the correct answer below.

Given two propositions p and​ q, the statement p or q is called their disjunction. It is false only if p and q are both false.

Which of the following is an example of a​ conjunction?

I have a voice and I can sing.

Which of the following is an example of a​ disjunction?

I have a voice or I can sing.

Which of the following is an example of a​ conditional?

If I have a​ voice, then I can sing.

Explain when​ 'p or​ q' is true. Select all that apply.

'p or​ q' is true when both p and q are true. ​'p or​ q' is true when p is true and q is false. ​'p or​ q' is true when p is false and q is true.

Define conditional. Choose the correct answer below.

Given two propositions p and​ q, the statement if​ p, then q is called their conditional. It is true in all cases except the case in which p is true and q is false.

What is the difference between an inclusive or and an exclusive​ or? Give an example of each.

An inclusive or allows either or both of the propositions. An exclusive or allows only one or the other proposition, but not both.

Determine if the following statement is a​ proposition, and give an explanation. Where do we go from here?

No, because the statement does not make a​ claim; it is a question.

Suppose the statement​ 'p or​ q' is true. Of what can you be​ certain? Explain your reasoning.

One or both of the statements are true. An​ 'or' statement is true if either or both propositions are​ true, and false only if both propositions are false.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning. When Sally is​ depressed, she listens to music. I saw her today listening to​ music, so she must have been depressed. Choose the correct answer below.

The statement does not make sense. Sally listens to music when she is​ depressed, but the statement does not clearly state that this is the only time Sally listens to music.

When are two statements logically​ equivalent? Explain your reasoning.

Two statements logically equivalent if they have the same truth values.

Explain when​ 'p and​ q' is true. Select all that apply.

​'p and​ q' is true when both p and q are true.