Chapter 4.4, Problem 44SPR

To determine

The truth value of given conditional statement, if statement is false, the counterexample for it.

Answer to Problem 44SPR

The given conditional statement is false as there is a counterexample.

Explanation of Solution

Given:

The given conditional statement is:

  $If{\text{ x}}^2=25,then\text{ x = 5}\text{.}$

Calculation:

Notice ${\left(-5\right)}^2=25\text{ and -5 }\ne \text{ 5}\text{.}$

Above is the counterexample of the given conditional statement $If{\text{ x}}^2=25,then\text{ x = 5}$ , the hypothesis is true and the conclusion if false.

Hence, the given conditional statement is false as there is a counterexample.