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Expert-verified Found in: Page 212 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved. If ${n}^{2}$ is not a multiple of 3, then n is not a multiple of 3.

Hence proved that if ${n}^{2}$ is not a multiple of 3, then n is not a multiple of 3.

See the step by step solution

## Step 1. Define contrapositive statement

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’.

The given statement is if ${n}^{2}$ is not a multiple of 3, then n is not a multiple of 3.

## Step 2. Let the given statement and find its contrapositive

The contrapositive of the given statement is if n is not a multiple of 3 then ${n}^{2}$ is not a multiple of 3.

## Step 3. Prove the statement

Suppose the values for n are 3,6,9.

Then the value of ${n}^{2}$ will be:

role="math" localid="1638187118341" $\begin{array}{c}{n}^{2}={\left(3\right)}^{2}\\ =9\\ {n}^{2}={\left(6\right)}^{2}\\ =36\end{array}$

Also, . Hence ${n}^{2}={\left(9\right)}^{2}=81$ is also the multiple of 3.

Hence proved. ### Want to see more solutions like these? 