Chapter 2.1, Problem 12WE

To determine

To prove:that the statement is false and give a counter example

Explanation of Solution

Given information:

The given statement is:

If $n^2=5n,$ then $n=5$

If $n^2=5n,$ then $n=5$

Counter example:

Consider $n=0$

Then

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

Also

  $5n=5\cdot 0=0$

Therefore $n^2=5n$

But $n\ne 5$

Thus, our statement is false

A counter example is such an example which shows the given statement is false

Therefore, the counter example is $n=0$