I have to provide direct proofs for the following and I am not sure how to do that.
1. If the square of an integer is odd then the integer must be odd.
Pf: Since the square of an integer is odd then there exists some integer c such that x^2 = 2c+1 where (2c+1) is an integer.
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.