The symmetric difference between two events A and B is the set of all sample points that are in exactly one of the sets A or B and is often denoted AAB. That is, define AAB = (ANB) U (ANB). (a) Prove that AAØ = A and AAA = Ø. (b) Prove that P(AAB) = P(A) + P(B) - 2P(ANB).