Consider a relation schema R A B C D E G and set of function

Consider a relation schema R (A, B, C, D, E, G) and set of functional dependencies: FD = {A BG, C D, CD E, G E, C E} that relations on schema R must satisfy. Find a lossless-join decomposition of R into BCNF. Do NOT do any unnecessary decompositions.

Solution

By calculating an attribute closure we can see the candidate keys are:

AB, BC, and BD

Attribute closure:

A -> A

B -> B

C -> ACD

D -> AD

AB -> ABCD

AC -> ACD

AD -> AD

BC -> ABCD

BD -> ABCD

CD -> ACD

ABC -> ABCD

ABD -> ABCD

ACD -> ACD

BCD -> ABCD

If we start to decompose on C->D then D->A and AB->C

If we start to decompose on D->A then AB->C