you are begging the question here. that is, you are assuming what you are supposed to be proving. hint, use the contrapositive. assume the integer is even, then what? (you know what "contrapositive" means right?)

you made the same mistake here...sort of. again, do the contrapositive. assume that x and y are not odd integers. that is, we have two cases, x and y are both even, or (without loss of generality) x is even and y is odd. what does that tell us about xy?2. If xy is an odd integer then x and y are odd integers.

Pf: Since xy is an odd integer then there exists some integer c so that xy = 2x+1.

Thats as far as I can get on either of those.

How are you with implications?