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Chapter 1: Q37. (page 57)

Example 4 Find a counterexample for each conditional statement.

If x2=1then x must equal 1.

Short Answer

Expert verified

The statement that If x2=1, then x must equal 1 is not true.

Step by step solution

01

Step 1. Given Statement.

If x2=1,then xmust equal 1.

02

Step 2. Description of step.

To find a counterexample for the given statement, solve the given expression and find the value of xas

x2=1鈬�x=卤1鈬�x=卤1鈬�x=1andx=鈭�1

03

Step 3. Conclusion.

So xhas two values, 1 and -1, but according to the given statement, xmust be equal to 1.

Therefore, the statement If x2=1,then xmust equal 1 is not true, and the counterexample is x=鈭�1.

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