5. (25 points total) Let R(A, B, C, D) satisfy the FDs AD, ABC, C D. (a) (5 points) List all the keys for R. (b) (10 points) List all BCNF violations. Give each violation in the form, S+ = T, where S and I are sets of attributes, T contains an attribute not in S, but T does not contain all attributes. (c) (10 points) Use the information in the last item to decompose R fully into BCNF. Your decomposition should be efficient. Give your decomposition in tree form, as depicted in class. (There are two correct answers; you should only give one of them.)