Chapter 2.1, Problem 23WE

To determine

To state: The converse of statement and state whether it is true or false

Answer to Problem 23WE

The statement is true.

The converse of the given statement is false

Explanation of Solution

Given information:

The given statement is:

  $a^2>9$ if $a>3$

  $″a^2>9$ if $a>3″$

Here the given statement is of the form $q$ if $p$

Here $\text{p}$ is $″a>3″$ and $\text{q}$ is $″a^2>9″$

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

Therefore, the statement is true.

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

Therefore, the converse of the given statement is

If $a^2>9$ then $a>3$

  $a=16$

  $a=\pm 4$

Here $a^2>9$

Consider $a^2=16$ which is greater than 9

But $a=\pm 4$

That is $a$ may be -4 which less than 3

Therefore, the converse of the given statement is false.