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Chapter 2: Q12 (page 35)

Provide a counterexample to show that each statement is false.

Statement: If n2=5nthen n=5.

Short Answer

Expert verified

For the counterexample n=0
, 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 n2=5n, then n=5.鈥� let the counterexample ben=0.

03

Step 3. Verify the counterexample.

Here,

n2=02=0

And,

5n=5脳0=0

Thus,n2=5n,

But, n鈮�5which contradicts the statement n=5.

Thus, if n2=5n, it does not necessary means n=5.

Therefore, for the counterexample n=0, the statement is false.

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