Let f: x --> y be a function. (a) prove the following: if a, b c x are sabseits, then f(aub) = f(a)us(b). (b) prove the following: if a, b c x are subsets then f(an b) s f(a)n f(b). (c) give an explicit example of a function : x y and subsets a, b c x which demonstrate that the equality f(anb) = f(a)n f(b) need not hold.