Help asap please!!!

Consider the following theorems and their proofs. Unfortunately, each proof has a mistake in it. Find the mistake in each proof, and explain why it is a mistake (you do not have to write a correct proof) a) Theorem: The sum of two odd integers is even. Proof Suppose x and y are two odd integers. If xy is even, then by the definition of even, there exists an integer k such that x +y 2k. Since x and y are odd, there exists an integer m such that x-2m+1, and an integer n such that y 2n+1. Therefore x+y=(2m+1)+(2n+1) = 2k By the definition of"even", x + y is even. QED b) Theorem: The sum of three integers that are divisible by 5 is divisible by 15. Proof: Suppose that x, y and z are integers that are divisible by 5. Then x - 5k for some integer k. Similarly, y-5k for some integer k, and z = 5k for some integer k. Thus x + y + z = 5k + 5k + 5k-15k, which is indeed divisible by 15