Consider the statement, "For all integers a and b, if the product of a and b is even, then a is even or b is even." What would be the beginning of a direct proof of this statement?

Group of answer choices

Assume that a is even or b is even. Then a or b = 2k for some integer k. We must show that either a is even or b is even, so it suffices to show one or the other.

Assume that ab is even. Then ab = 2k +1 for some integer k. We must show that either a is even or b is even, so it suffices to show one or the other.

Assume that ab is even. Then ab = 2k for some integer k. We must show that either a is even or bis even, so it suffices to show one or the other.

Assume that ab is even. Then ab = 2k for some integer k. We must show that a is even and b is even.