Question

This question is from the subject: Database Systems

QUESTION 8 Consider the relation R(A,B,C,D,E,F) with FDs A -> C,B->D, C-> E, D -> F. Consider the BCNF status of R. Which of the following could be correct given the information above? 1. Ris in BCNF already. 2. Ris not in BCNF. It must be divided into R1(A,C,E) with FDs A->C, C-> E, and R2(B,D,F) with FDs B -> D, D -> F. 3. R is not in BCNF. It must be divided into R1(C,E) with FDs C -> E, R2(D,F) with FDs D -> Fand R3(A,B). 4. Ris not in BCNF. It must be divided into R1(A,C,E) with FDs A->C, C-> E, R2(B,D,F) with FDs B->D, D-> F, and R3(A,B)

Answer 1

For the given relation R(A,B,C,D,E,F) which contains the functional dependencies FDs like A-> C,B -> D, C -> E and D -> F in which A is functionally dependent on B,B is functionally dependent on attribute D, C is functionally dependent on E and finally D is functionally dependent on F.

From this relationship,it can be concluded as each attribute A,B,C and D contains unique values in which each attribute contain primary key.To avoid repetition the relations like A-> C,B -> D, C -> E and D -> F does not satisfy BCNF.The attributes like C and D may satisfy multivalued dependency i.e., MVD. Hence,the above relationship does not satisfy Boyce Codd Normalization Form(BCNF).

So to satisfies the relationship R1(C,E) with FDs C -> E, R2(D,F) with FDs D-> F and R3 (A,B). in which C,D and A contain primary keys.

So option (3) is correct.