5. More on decomposition (24 points total). Consider relation R(ABCDE) and F = {AC-> B, B ->D, D->E}. Suppose the original relation R is decomposed (regardless which algorithm is used) into R1 (ABD) and R2 (BCE).

(a) [6] Compute F1 and F2 (i.e., identify FDs projected into two smaller relations R1 and R2).

(b) [3] Is R1 in 3NF? Explain.

(c) [3] Is R2 in 3NF? Explain.

(d) [6] Is this decomposition (from R into R1 and R2) a lossless-join decomposition? Justify your answer.

(e) [6] Is this decomposition dependency preserving? Justify your answer.