Relation RABCDE Suppose that Functional Dependency Set FD is

Relation R(A,B,C,D,E) Suppose that Functional Dependency Set FD is {AB->D, A->C, B->E, B->A, CE->B}

1) Show B is key

2) Show another key (except B)

3) Is R satisfy BCNF? if not, show that all functional dependencies which are violating BCNF.

Solution

Given Relation R(A,B,C,D,E) with Functional Dependency Set FD is {AB->D, A->C, B->E, B->A, CE->B}

1) B is key because it gives you all of the attributes of the relation.

B->E, B->A, A->C, AB->D, CE->B

B->ABCDE

So B is a key.

2) another key can be CE

CE->B, B->E, B->A, A->C, AB->D

CE -> ABCDE

So CE is a key because it gives you all of the attributes of the relation.

3) R does not satisfy BCNF because candidate key is B and unfortunately all the left hand side FDs does not include B, so the relation is not in BCNF.

Functional dependencies which are violating BCNF :-

A->C,

CE->B