Chapter 2: Q12 (page 35)

Provide a counterexample to show that each statement is false.
Statement: If $n^{2} = 5 n$ then $n = 5$ .

Short Answer

Expert verified

For the counterexample $n = 0$
, the statement is false.

Step by step solution

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.

Step 2. State counterexample.

For the given statement “If $n^{2} = 5 n$ , then $n = 5$ .” let the counterexample be $n = 0$ .

Step 3. Verify the counterexample.

Here,

$\begin{matrix} n^{2} = 0^{2} \\ = 0 \end{matrix}$

And,

$\begin{matrix} 5 n = 5 \times 0 \\ = 0 \end{matrix}$

Thus, $n^{2} = 5 n$ ,

But, $n \neq 5$ which contradicts the statement $n = 5$ .

Thus, if $n^{2} = 5 n$ , it does not necessary means $n = 5$ .

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

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Provide a counterexample to show that each statement is false.
Statement: If $n^{2} = 5 n$ then $n = 5$ .

Short Answer

Step by step solution

Step 1. Define counterexample.

Step 2. State counterexample.

Step 3. Verify the counterexample.

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Provide a counterexample to show that each statement is false.Statement: If n2=5nthen n=5.

Short Answer

Step by step solution

Step 1. Define counterexample.

Step 2. State counterexample.

Step 3. Verify the counterexample.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Decision Maths

Statistics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Provide a counterexample to show that each statement is false.
Statement: If $n^{2} = 5 n$ then $n = 5$ .