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Archangel Macsika

Give a contrapositive proof of the theorem; "If n is an interfer and 3n + 2 is even, then n is even."?

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Let us give a contrapositive proof of the theorem: "If n is an interger and 3n + 2 is even, then n is even.".

For this suppose that n is an interger and 3n + 2 is even, but n is not even, and hence n is odd. Then n=2k+1 for some k\in\mathbb Z. It follows that 3n+2=3(2k+1)+2=6k+3+2=(6k+4)+1=2(3k+2)+1, where 3k+2 is integer. Therefore, 3n+2 is odd. We conclude that 3n+2 is not even, that is we have a contradiction with initial assumption that 3n + 2 is even.


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Question ID: mtid-5-stid-8-sqid-3105-qpid-1804