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Math Help - Odd Product Proof

  1. #1
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    Odd Product Proof

    So I did this wrong, but I wondering what the correct way would be.
    Odd Product Proof-hwredo2.jpg
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  2. #2
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    Re: Odd Product Proof

    Proof by contrapositive:
    [A] All integers are odd or even
    [B] if at least one of x,y are even then xy must be even (you should prove this, but it is trivial).

    Since xy is odd then the conditions in [B] have not occured, ie neither X nor Y is even
    so, by [A], both X and Y are odd.


    Proof by exhaustion:
    there are only 4 possible cases for (x,y): (odd,odd),(even,odd),(odd,even),(even,even).

    its easy to determine the evenness of xy in each case, and you can prove/disprove any statement you want from the results.
    Last edited by SpringFan25; April 9th 2012 at 02:10 PM.
    Thanks from renolovexoxo
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