Consider the table R(B,C,D,E) with the following FDs BC E, CED, E B, D E. (a) (3 marks) Find all the keys of R. (b) (5 marks) Is R in 3NF, why? (c) (3 marks) Which FDs violate BCNF, why? (d) (7 marks) Decompose R into a collection of relations that are in BCNF and lossless. (e) (2 marks) Which FDs are not preserved by the decomposition in (d)?