So I did this wrong, but I wondering what the correct way would be.Attachment 23550

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- Apr 9th 2012, 01:51 PMrenolovexoxoOdd Product Proof
So I did this wrong, but I wondering what the correct way would be.Attachment 23550

- Apr 9th 2012, 02:00 PMSpringFan25Re: 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.