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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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Most popular questions from this chapter

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

Statement: If x2=4,thenx=鈭�2.

Justify each step.

x鈭�2=2x+85

5x鈭�2=2x+8

5x鈭�10=2x+8

3x鈭�10=8

3x=18

x=6

State the number that is paired with the bisector of 鈭�CDE.

State which definition, postulate, or theorem justifies the statement about the diagram.

If BD炉鈮�DC炉, then D is the midpoint of BC炉.

State the hypothesis and the conclusion of each conditional.

If , then .
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