Question

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

$a^2>9$if $a>3$.

Short answer

The statement "$a^2>9$if $a>3$", " is true.

The converse of the given statement “If$a^2>9$ then $a>3$.” is false.

Step-by-step solution

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 “If p, then q” will be “If q, then p”.

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

The statement "$a^2>9$ if $a>3$", Here the given statement is of the form q if p.

Here p is and q is $a^2>9$.

If $a>3$obviously $a^2>9$.

Therefore, the statement is true.

Step 3. Write the converse.

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

Therefore, the converse of the given statement is – “If $a^2>9$then $a>3$.”

Step 4. State whether the converse is true or not.

In order to verify if the converse is true or not let $a^2=16$such that $a^2>9$.

But $a=\pm 4$.

That is a maybe –4 which is less than 3.

Therefore, the converse of the given statement is false.