Chapter 6: Q22. (page 212)

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.

Short Answer

Expert verified

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

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

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

Hence proved.

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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.

Short Answer

Step by step solution

Step 1. Define contrapositive statement

Step 2. Let the given statement and find its contrapositive

Step 3. Prove the statement

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Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved.If n2is not a multiple of 3, then n is not a multiple of 3.

Short Answer

Step by step solution

Step 1. Define contrapositive statement

Step 2. Let the given statement and find its contrapositive

Step 3. Prove the statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Geometry

Decision Maths

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

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.