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database-designbcnf

Is my application of Boyce-Codd NF correct in this exercise?

EXAM revision, not homework.

I'm working on this exercise and I would like to check is my solution okay:

Given the following relationship, R, and set of functional dependencies, F: R = {A,B,C,D,E,F,G,H,I} F= { {C,D} -> {A}, {G} -> {E}, {C,D,E} -> {G,B,H}, {B} -> {F}, {H} -> {I} } decompose R into relations that satisfy Boyce-Codd normal form.

My answer: BOLD is primary key

(C,D,A)

(C,D,E,B,H)

(B,F)

(H,I)

(G,C,D)

(E,G)

Solution

  • I think the first four you derived are all in 5NF.

    • {G CD}
    • {EG}

    But these two don't look right.

    For one thing, one of your FDs is G->E. In a relation that contains only G and E, how did you determine that the right decomposition is

    • {EG}

    instead of

    • {G E}

    given that the FD G->E still has to hold?

    At a glance, I don't see how you can derive G->CD from the FDs you gave.