Consider a relation R with five attributes A, B, C, D, and E. You are given the following functional dependencies: A --> B, BC --> E, and ED --> A.

Is R in BCNF? If it is not, decompose it into a collection of BCNF relations.

For this, R is not in BCNF because none of A, BC, and ED contain a key. It cannot decompose into BCNF as other violations like AC, BD, or CD do not satisfy BCNF. If we further decompose it like ABC, or ABD, these relations also are not in BCNF.

So how is it decomposed into a collection of BCNF?