I've been having some trouble with this question, I'm hoping someone could tell me if I'm on the right path.

Given the sets A, B, E, F, M and N where and , and the function , show whether the following equalities hold:

a)

b)

For part a I've done this:

Let

If I'm understanding this right A,B and E,F are proper subsets of M and N respectively, so the function f could map values between M and N that aren't in the union of A,B or E,F. But in part b) for instance f is being applied to a subset of M (A u B) and so any values outside this subset but still part of set M are irrelevant for the proof, right?

So is the proof for a) complete?