2.Consider a relation R(A,B,C,D,E) satisfying the following dependencies: A->B, BC->E,ED->A. (a) List all keys for R. (b) Is R in 3NF? Justify your answer. (c) R is not in BCNF. Explain why? (d) Show the first step in a BCNF decomposition of R, including computing the projection of the dependencies onto the decomposed relations, and identifying keys for each subrelation. (e) Is the above decomposition lossless? Is it dependency-preserving? Are the subrelations in BCNF? 3NF? Explain each of your answers BRIEFLY. (f) Repeat step (d), if necessary, till you have decomposed R into BCNF relations. (g**) Argue whether there is a decomposition that preserves dependencies.