Exercise 4. (FROM EXAM 1, FALL 2015) For each of the following relations, determine which is valid for arbitrary events A, B, and C. (Note: to be true "for arbitrary events", it must be true for any such event. Use a Venn diagram if it is helpful.) (On the exam, this was a True/False question. For this homework, show whether it is true or false.) (a) (AUBUC) = AUBUC (b) (ANB) U (An Be) U (An B) = (An Be)e (c) (AB) CA- (B-C). (d) (AUB)n (AUB) = (ANB) U (ANB) U (An Bnce) Hint: be careful, item (d) is tricky.