Chapter 2.1, Problem 24WE

To determine

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

Answer to Problem 24WE

The statement is true.

The converse of the given statement is false

Explanation of Solution

Given information:

The given statement is:

  $″x=1,$ if $x^2=x″$

  $″x=1,$ if $x^2=x″$

Here $x=1$

Then $x^2=1=x$

Therefore, the statement is true.

Here $\text{p}$ is $″x=1″$ and $\text{q}$ is $″x^2=x″$

The converse is of the form "if $q$ , then $p\text{"}$

Therefore, the converse of the given statement is;

If $x^2=x,$ then $x=1$

Here $x^2=x$

Then $x$ may be 0 or 1

That is, $x$ may be 0

Therefore, the converse of the given statement is false.