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Chapter 2: Q13 (page 34)

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

If , then .

Short Answer

Expert verified

The converse of the given statement is "If then 鈥� and the converse is false.

Step by step solution

01

Step 1. Converse of 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�.

02

Step 2. Write the converse of the statement.

"If , then 鈥�

The square of a positive term is positive.

Therefore, the statement is true.

Consider p is and q is

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

Therefore, the converse of the given statement is;

" If then 鈥�

03

Step 3. Verify the converse of the statement.

If then x may be positive or negative. Thus, is also a possibility.

Therefore, the converse of the given statement is false.

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Proof:

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