Problem 2 (45 Points) For the relational schema given below and its corresponding functional dependencies (FDs) R(A, B, C, D, E) S = { B → A, B → E, CE → D, D → B} answer the following questions: a. (5 Points) find all candidate keys of the relation through an exhaustive set of attribute closures. Note when an attribute set closure is trivial. b. (5 Points) Given the keys you defined in step 1, find the FDs (from the given ones) that violate BCNF. (15 Points) Decompose the relations to satisfy BCNF. Specify which FD is used to make the decomposition. If there is multi-step decomposition, then indicate each step along with which FD is used for the decomposition. d. (20 Points) If the FDs are not in 3NF, calculate a minimal basis for the FDs and decompose the relations to satisfy 3NF.
