Question

If x and y are odd integers, then x+y is even. Give a proof by contradiction of this theorem

Answer 1

Start off by assuming \(x+y\) is odd, and show that \(x\) and \(y\) can't both be odd integers.

For starters, you would write \(x+y=2k+1\) for some integer \(k\). Can you express this in terms of the sum of two odd integers?