Chapter 6.2, Problem 22WE

To determine

To prove :If $n^2$ . is not multiple of $3,$ then $n$ is not multiple of $3.$

Explanation of Solution

Given information:

  

If $n^2$ . is not multiple of $3,$ then $n$ is not multiple of $3.$

Calculation:

Consider the following statement:

If $n^2$ . is not multiple of $3,$ then $n$ is not multiple of $3.$

Prove the above statement by proving following contrapositive.

If $n$ is a multiple of $3,$ then $n^2$ is a multiple of $3,$

Suppose $n$ is equal to 3,6 and9.

Then the value $n^2$ is as follows:

Value of $n^2$ when $\text{n}$ is equal to 9 is as follows:

  $\begin{array}{c}n²={\left(9\right)}^2\\ =81\end{array}$

Hence, above statement is proved.