I just have a very quick (and simple) question: When trying to prove equalities like [itex]A \cup (B \cup C) = (A \cup B) \cup C[/itex], is it sufficient to note that both sets consist of all elements [itex]x[/itex] such that [itex]x \in A[/itex], [itex]x \in B[/itex] or [itex]x \in C[/itex]? Or do I need to go through proving that each set is a subset of the other and consequently deduce that the two sets are equal? I already know that the second procedure works and although the first one seems make intuitive sense, I'm concerned that it isn't considered sufficient or formal. I would appreciate any feedback. Thanks!