Question

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If , then

Short answer

The counterexample is .

Step-by-step solution

Step 1. Define counterexample.

The counterexample is an example for which a hypothesis is true but the conclusion is false for an if-then statement.

Step 2. Observation of the statement.

In order to find a counterexample for the statement “If , then .” we need to find a value of x such that , but .

Step 3. State the counterexample.

Take square root on both sides of the equation ,

That is

Thus, x can be either 7 or –7.

So, for , .

Therefore, the number –7 is a counterexample.