2. (a) For events A, B, prove that P(AUB) = P(A) + P(B) -P(AnB) . (b) For events A, B, C, prove that P(AUBUC) =P(A) + P(B) + P(C) -P(AnB) -P(AnC) -P(BAC) +P(AnBnc) . (c) For events Al, A2, . .. An, prove that IC(1,...,n} where A/ :=nic, A; is the intersection of all A; such that i ( 1. Hint: Use induction