Convert to BCNF

Question

I am given the following ratio:

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

and the following functional dependencies:

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

I am trying to convert this to a BCNF form.

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

 Keys: ABC, BCD, BCE 

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

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

At this point, I believe that relationships in the form of BCNF are lossless, but not dependency conservation.

Does this sound like the right technique for this kind of thing? Maybe I skipped one or two steps?

Answer 1

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

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

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