I need help with this Problem. Thanks! Short Proofs 3. Result: For every integer n, 4n...

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Question

I need help with this Problem. Thanks!
Short Proofs 3. Result: For every integer n, 4n + 7 is odd.

Answer 1

Answer #1

If possible, let $\left ( 4n+7 \right )$ is not odd for some .

Then it must be even and , it can be written as 4n+7=2m ,for some integer .

This implies , $2\left ( m-2n \right )=7$ .

This , shows that, is an even number, which is not possible.

Hence, our assumption was wrong.

Therefore, $\left ( 4n+7 \right )$ is odd for every integer .

Answer 2

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