Given a relational schema R with attributes A, B, C and D where the functional dependencies AB -> C, C -> D, and D -> A are supposed to hold.

(20 points) Given a relational schema R with attributes A, B, C and D where the functional dependencies AB >C,CD, and D>A are supposed to hold. (a) Is R in BCNF? If yes, explain why. If not, list all violations. (b) If R is NOT in BCNF, give it a lossless BCNF decomposition. (c) Does your decomposition in (b) preserve the given functional dependencies? 6. Explain. (d Give a 3NF decomposition for R (e) Does your decomposition in (d) preserve the given functional dependencies? Explain