5. (a) For n ? 2 give a recursive definition of the union A? U A? U ... U A? and the
intersection A? ? A? ? ... ? A? of the sets A?, A?, ..., A?. (Hint: Example 4.1.5.)
(b) Let A, B, C be sets. Use your definition in A to (help) prove that (A?B?C)? =
(A? U B? U C?).