2. Let X be a set and A be a subset of X. The indicator function of A, denoted XA, is the function from X to {0, 1}, given by 1 if xEX XA(x) = if xEX A (Symbol x is a Greek letter chi.) (a) Give an explicit example of sets X and A where the function XA : X - {0, 1} is surjective. (b) Give an explicit example of sets X and A where the function XA : X - {0, 1} is injective. (c) Prove that for all subsets A and B of X, and all r E X, XAUB(X) = XA(X) + XB(X) - XAnB(2)