Consider the relation scheme R = {A, B, C, D, E, G} and the set of functional dependencies for the relation R are F = {AB C, AC B, ABD E, D B, BC A, E G}.

a) Find all candidate keys of F.

b) Derive a canonical cover for F in a systematic manner.

c) Find a 3NF decomposition for R that is lossless and dependency preserving.

d) is R in BCNF? if it is not in BCNF, find a BCNF Decomposition that is lossless. Is your BCNF decomposition in (c) dependency-preserving?

e) If R is decomposed into {ABC, ACDE, ADG}, will the decomposition lead to a lossless-join? Is the dependency preserved (if-any)?