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Chapter 2: Q12 (page 34)

State the converse of each conditional. Is the converse true or false?

If today is Friday, then tomorrow is Saturday.

Short Answer

Expert verified

The hypothesis is and the conclusion is .

Step by step solution

01

Step 1. Hypothesis and the conclusion of a conditional.

The hypothesis and the conclusion of a conditional statement are where the hypothesis is the phrase immediately following by the word if and the conclusion is the phrase immediately following by the word then.

02

Step 2. Converse a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement 鈥淚f p, then q鈥� will be 鈥淚f q, then p鈥�.

03

Step 3. Write the converse of the statement.

If today is Friday, then tomorrow is Saturday.

The day after Friday is Saturday.

Therefore, the statement is true.

Consider p is "today is Friday" and q is "tomorrow is Saturday"

The converse is of the form "if q, then p鈥�.

Therefore, the converse of the given statement is;

If tomorrow is Saturday, then today is Friday

04

Step 4. Verify the converse of the statement.

It is known that the day before Saturday is Friday

Therefore, the converse of the given statement is true.

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Most popular questions from this chapter

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If a line lies in a vertical plane, then the line is vertical.

Tell whether each statement is true or false. Then write converse and tell whether it is true or false.

Statement: If b>4then5b>20

What can you conclude if the following sentences are all true?

  1. If(1) p, then q.
  2. (2) p
  3. I(3) q, then not r.

(4) s or r

State the hypothesis and the conclusion of each conditional.

If , then.

Justify each step.

23b=8鈭�2b

2b=38鈭�2b

2b=24鈭�6b

8b=24

b=3
See all solutions

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