(a) Using the closure algorithm, compute the closure of B,C]. For full credit, show each step in the algorithm. (b) Is {B, C} a key for R(A, B,C, D, E)? Why or why not? (c) Decompose relation R(A, B,C, D, E) into BCNF. For full credit, show each step of the transformation, and also the FDs for each of the (temporary and final) relations that R(A,B.C,D.E is decomposed into. The FDs are reproduced below for your conveniences (d) Is the decomposition n lossless? Why or why not? (e) Does the decomposition preserve FDs? Why or why not