Question

Provide a counterexample to show that each statement is false.

Statement: If $n^2=5n$then $n=5$.

Short answer

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 $n^2=5n$, then $n=5$.” let the counterexample be$n=0$.

Step 3. Verify the counterexample.

Here,

$\begin{array}{c}{n}^2=0^2\\ =0\end{array}$

And,

$\begin{array}{c}5n=5\times 0\\ =0\end{array}$

Thus,$n^2=5n$,

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

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

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