contestada

a) Indicate all the BCNF violations. Do not forget to consider FD’s that are not in the given set, but follow from them. However, it is not necessary to give violations that have more than one attribute on the right side?
b) Decompose the relations, as necessary, into collections of relations that are in BCNF?
o R(A,B,C,D) with FD’s AB ->C, BC ->D, CD ->A and AD ->B
o R(A,B,C,D) with FD’s A ->B, B ->C, C ->D and D ->A
o R(A,B,C,D,E) with FD’s AB ->C, C ->D, D ->B, and D ->E

Respuesta :

R(A,B,C,D,E) has the following FDs: AB->C, DE->C, and B->D. R(ABC) and R are the decomposed relations into BCNF (BCDE).

i) ABE is a candidate key for the relation presented.

The above relation does not fall under BCNF since the left-hand sides of the functional dependencies, AB C, DE C, and B D, do not contain super keys.

Thus, BCNF is violated by all FDs.

ii) R(ABCD), R(CDE), and R are the decomposed relations into BCNF (ABE).

FD's AB-> C, C-> D, D-> B, and D->E are present in R(A, B, C, D, and E).

I AB, AC, and AD are the potential keys for the given connection.

As AB C has the super key on the LHS of the functional dependencies, it does not go against the BCNF. Due to the lack of super keys on their LHS, C, D, and E violate the BCNF.

ii) R(ABC) and R are the decomposed relations into BCNF (BCDE).

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