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Chapter 2: Q25 (page 35)

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

n>5only if n>7.

Short Answer

Expert verified

The statement "n>5 only if n>7", " is false.

The converse of the given statement 鈥淚fn>7 then n>5.鈥� is true.

Step by step solution

01

Step 1. 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�.

02

Step 2. State whether the statement is true or not.

The statement "n>5only if n>7", Here, the given statement is of the form p only if q.

Here p is n>5and q is n>7.

If n=6, it is greater than5 but not greater than 7, therefore the statement is false.

03

Step 3. Write the converse and verify if it is true or not.

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

Therefore, the converse of the given statement is 鈥� 鈥淚fn>7 then n>5.鈥�

Clearly, all n greater than 7 must be greater than 5. Therefore, the converse of the statement is true.

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