Chapter 2.1, Problem 18WE

To determine

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

Answer to Problem 18WE

The statement is true.

The converse of the given statement is false

Explanation of Solution

Given information:

The given statement is:

"If $x^2=4$ then $x=-2″$

"If $x^2=4$ then $x=-2″$

Here, $x^2=4$

Then,

  $x=\pm 2$

That is $x$ may be $x=+2$

Therefore, the statement is false.

Consider $p$ is $″x^2=4$ and $q$ is $″x=-2″$

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

Therefore, the converse of the given statement is;

If $x=-2$ then, $x^2=4$

Here,

  $x=-2$

Then, $x^2=4$

Therefore, the converse of the given statement is true.