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Chapter 2: Q11 (page 34)

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

If , then

Short Answer

Expert verified

The counterexample is .

Step by step solution

01

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.

02

Step 2. Observation of the statement.

In order to find a counterexample for the statement 鈥淚f , then .鈥� we need to find a value of x such that , but .

03

Step 3. State the counterexample.

Take square root on both sides of the equation ,

That is

Thus, x can be either 7 or 鈥�7.

So, for , .

Therefore, the number 鈥�7 is a counterexample.

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