Oh I see, I got one more question to ask though:
Conjecture: The product of an even integer with an odd integer is even.
Proof(Direct): Let a be an even integer and let b be an odd integer. Because a is even, a = 2p for some integer p. Because b is odd, b = 2q + 1 for some integer q. If ab is even, then there exists an integer r such that ab = 2r. Thus, ab = (2p)(2q + 1) = 2r. As ab is equal to twice r, ab must be even.
Therefore, the product of an even integer with an odd integer is even
What is actually wrong with this proof??
My guess is because it tries to prove the other way around, it tries to proof if the product of two integer is even then one integer must be odd and the other must be even. Am I right??