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Show that if n is an integer and n$3+5$ is odd, then n is even using

a proof by contraposition.

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Then, n$3+5=(2$k $+1)3+5=8$k$3+12$k$2+6$k $+6=2(4$k$3+6$k$2+3$k $+3).$Then, n$3+5=(2$k $+1)3+5=8$k$3+12$k$2+6$k $+6=2(4$k$3+6$k$2+3$k $+3).$ open choices for ranking

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Thus, if n is odd, then n$3+5$ is even.Thus, if n is odd, then n$3+5$ is even. open choices for ranking

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As n$3+5$ is two times an integer, it is even.As n$3+5$ is two times an integer, it is even. open choices for ranking

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Assume that n is odd.Assume that n is odd. open choices for ranking

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We can write n $=2$k $+1$ for some integer k$.$