Consider a relation schema R(A, B, C, D, E, F, G, H), with functional dependencies {FH -> HGB, GA -> CD, C -> E, B -> D, FG -> D}. a) Find a minimal cover for the FDs. b) Is the dependency FHA -> GB implied by the FDs? c) Is the decomposition into FHGAB and GABCDE lossless? d) Is the above decomposition dependency preserving?

e) Is there a lossless, dependency preserving decomposition of this schema into BCNF? If so, exhibit one. If not, explain. f) Is there a lossless, dependency preserving decomposition of this schema into 3NF? If so, exhibit one. If not, explain.