Prove:
A × B = ∅ if and only if A = ∅ or B = ∅.
i would do this by proving the forward direction using the contrapositive, and the converse via a direct proof.
at some point in your text you should have it written that for every set . this should help you prove the converse directly.
for the forward direction, assume NOT or . then by DeMorgan's laws, we have that AND . now if both and are nonempty, what can you say about ?