I think I'm on the right track, it seems like such an easy proof but oh well!

Anyway here's what I got so far.

Suppose A=B=∅

= ∅

= ∅ U ∅

= A U B

(I think that's a proof, atleast I think that's how my professor did it)

Suppose A U B = ∅

Case 1: x is in A

x is in A, x is not in B

Therefore A U B <--> ∅

[(for all x in (A U B), x is in ∅) And (for all x in ∅, x is in (A U B)]

Since x is in a, in order for A U B = ∅

A = ∅

Case 2: x is in b

etc.

Im really confused, that doesnt seem to prove anything, I think I'm doing something wrong, any help?