Suppose B1, B2, . . . , Bk are events in a sample space S such that B1, B2, . . . , Bk are disjoint and B1 B2 . . . Bk = S. (a) (10 points) If A is any event in S, show that B1 A, B2 A, . . . , Bk A are all disjoint. (b) (10 points) If A is any event in S, show that [ k i=1 (Bi A) = A Similar to our proofs in class, please justify each line in your proof by writing the definition, assumption, or theorem you are using.