Consider a relation with schema R(A, B, C, D) and FD's A->B , B->C, and D->A.
a) What are all the nontrivial FD's that follow from the given FD's? You should restrict yourself to FD's with single attributes on the right side.
b) What are all the keys of R?
c) What are all the superkeys for R that are not keys?
d) Indicate all the BCNF violations. Do not forget to consider FD's that are not in the given set, but follow from them. However, it is not necessary to give violations that have more than one attribute on the right side.
e) Decompose the relations, as necessary, into collections of relations that are in BCNF.