why, yes

here's a hint. show that and then show . this will prove the equalityShow (A U B) X C = (A X C) U (A X B)

there is no way we can know this without knowing how A, B, and C relate to each other. clearly if B = C or either is a subset of the other, then this is not the case.And Show that AXC and AXB are disjoint

and please start using more descriptive titles than just "proof"