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Chapter 2: Q11 (page 35)

Provide a counterexample to show that each statement is false.

Statement: If , then .

Short Answer

Expert verified

For a counterexample, and , the statement is false.

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. State counterexample.

For the given statement 鈥淚f ab<0, then a<0.鈥� let the counterexample be a=2and b=鈭�1.

03

Step 3. Verify the counterexample.

Here,

ab=2脳鈭�1=鈭�2

So,ab<0ab<0

But, a=2>0, which contradict the statement a<0,

Thus, if ab<0, it does not necessary means a<0.

Therefore, for counterexample a=2and b=鈭�1, the statement is false.

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