Question

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

Statement: If $x^2=4$,then$x=-2$.

Short answer

The statement “If $x^2=4$,then $x=-2$.” is false, but the converse “If $x=-2$, then $x^2=4$,” is true.

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.

If $x^2=4$,then

$\begin{array}{c}x=\sqrt{4}\\ =\pm 2\end{array}$

Thus, x may be $+2$as well. Hence, the statement is false.

Step 3. Write the converse of the statement and verify.

The converse of the statement is: If $x=-2$then$x^2=4$,

Here,

If $x=-2$, then

role="math" localid="1637650485182" $\begin{array}{c}{x}^2={\left(-2\right)}^2\\ =4\end{array}$

Thus, the converse statement is true.

Therefore, the statement: " If $x^2=4$then $x=-2$" is false, but the converse of the statement: "If $x=-2$then $x^2=4$" is true.