Convert To BCNF

Question

I'm given the following relation:

R(A,B,C,D,E)

and the following Functional Dependencies:

F1 - AC -> D
F2 - D -> E
F3 - E -> A

I am attempting to convert this to BCNF form.

The first step I took was to figure out the possible keys for the relation.

Keys: ABC, BCD, BCE

Then I checked to see if the functional dependencies fit BCNF form, they do not. So I attempted to decompose and got the following:

R1(A,C,D) AC->D Keys: AC
R2(D, E) D->E Keys: D

I believe at this point that the relations are in BCNF form and are lossless, but are not dependency preserving.

Does this seem like the right technique for this sort of thing? Is there a step or two I might have missed?

Answer 1

I believe there is an error in your BCNF. Between R1 and R2, you've lost B.

Keys, ABC, BCD and BCE are correct. (You require B, C and one of either A, D or E).

R1 (A, B, C, D), key ABC and R2 (D, E) with key D is a valid normalization.