Consider a relation R = (A, B, C, D), and functional dependency set F = {AB ? C, C ? D, D ?A}.

a) Is F a minimal cover? Explain.

b) Compute F+.

c) List all the super keys of R.

d) List all the candidate keys of R.

e) Is R in 3NF given F? If it is not in 3NF, give a lossless dependency preserving decomposition of R with respect to F.

f) Is R in BCNF with respect to F? Justify your answer. If it is not in BCNF then give a BCNF lossless- join decomposition of R with respect to F which is also dependency preserving if possible.

g) Check if the decomposition you found in f) is dependency preserving or not.

h) Show that for all decompositions you make in f) are lossless join decompositions.