Problem 1 (35 Points) For the relational schema given below and the corresponding functional dependencies (FDs) R(A, B, C, D, E) S = {AB E, B C, B D, CE A}, answer the following questions: a. (10 Points) find all candidate keys of the relation R through an exhaustive set of attribute closures. Note when an attribute set closure is trivial. b. (5 Points) Assume that S is a minimal basis for R. List the dependencies that violate 3NF, if any. C. (5 points) If R is NOT in 3NF, decompose it into multiple relations that are in 3NF. d. (5 points) List the dependencies, in the order given in S, that violate BCNF. e. (10 points) If R is not in BCNF, provide decomposition into multiple relations where each one is in BCNF. For each decomposition step, use the first FD violation following the FD order given in S. For example, if AB E and B Care in BCNF but the other two FDs are in violation, then you would use B = D for the decomposition. Make sure to specify which FD is used to make the decomposition