Prove that if n is an integer and 3n + 2 is even, then n is even using a proof by contradiction.

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elverku7 · Accepted Answer

Proof by contradictionSuppose that 3n + 2 is even and 7 is not even. Because 7 is not even then 7 is odd. By the definition of odd numbers, there is an integer k such thatn=2k+1.Substituting n=2k+1 into 3n+2, we get3n+2=3(2k+1)+2=6k+3+2=6k+4+1=2(3k+2)+1.Thus, we can find an integer l=3k+2 such that3n+2=2l+1.That means, 3n+2 is odd.So far, our assumption, &#039;&#039;n is odd&#039;&#039;, leads us to the contradiction that 3n + 2 is both even and odd. This is a contradiction. Hence, &#039;&#039;n is odd&#039;&#039; must be a false statement. This completes the proof that n must be an even number.Result:Assume that 3n+1 is even and n is not even, and then derive a contradiction.

Prove that if n is an integer and 3n + 2 is even, then n is even using a proof by contradiction.

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