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Math Help - help with a proof

  1. #1
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    help with a proof

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

    I end up with 2f+1, where f is 3k+1, closed under multiplication and addition. Making it odd, which is not contradicting the assumption that n is odd.

    Where did I go wrong?
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  2. #2
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    Quote Originally Posted by lm6485 View Post
    Prove that if n is an integer and 3n+2 is even, then n is even using contradiction.

    I end up with 2f+1, where f is 3k+1, closed under multiplication and addition. Making it odd, which is not contradicting the assumption that n is odd.

    Where did I go wrong?
    To prove by contradiction, assume 3n+2 is even and n is not even then produce a contradiction. So, n = 2k+1 for some integer k. 3n+2 = 3(2k+1)+2 = 6k+3+2 = 6k+5 = 2(3k+2)+1. So 3n+2 is even and odd; contradiction.
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