Question 2: Decomposition [7 marks Consider a relation S on attributes (A, B,C, D, E) and the following functional dependencies. AB D BCD EA The relation S meets the conditions for 3NF but not BCNF (a) Give a decomposition of S into BCNF (use S1, S2,. to name the new relations) (b) Does your decomposition from part (a) preserve functional dependencies? Justify your answer. (c) Which (if any) of the following decompositions have a lossless join under the FDs above? Decomposition 1 RI(A, C, D), R2(A, B,C), R3(B,C, D, E) Decomposition 2 Ri(A, D, E), R2(A, B,C, D), R3(A, B, E) Decomposition 3 R1(A, C, D), R2(B, C, D), R3(A, B, C, E)