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Q22.

Expert-verified

Geometry

Found in: Page 212

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

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 by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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" $\begin{matrix} n^{2} = {(3)}^{2} \\ = 9 \\ n^{2} = {(6)}^{2} \\ = 36 \end{matrix}$

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

Hence proved.

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