dbms

Question

Consider the relation schema R(A,B,C), which has the FD B → C. If A is a candidate key for R, is it possible for R to be in BCNF? If so, under what conditions? If not, explain why not.

Answer 1

Let FD is given like this X----> Y
Only condition required for BCNF is X should be Super key of Relation.

Here B---> C is given and A is candidate key .
For BCNF relation B should also be key.

Comments

Thnx

Answer 2

If A is the candidate key for the given relation then the non trivial dependency that will be implied is :

A --> BC as we know candidate key is a key that uniquely identifies a tuples hence determines all attributes value

So prime attribute : A

Non prime attribute : {B,C}

And given we have other dependency : B --> C

So since B is not a superkey (not even a candidate key , as it does not determine all attributes), the given relation is not in BCNF

since for BCNF we require that every determinant (left hand side of FD) must be a superkey which is not the case here.

A superkey is nothing but superset of candidate key (or) we can say candidate key is the minimal superkey.

Comments

Thnx dada

Answer 3

Relation R is not in BCNF. A is not present in left side of FD B->C. For BCNF, left side of each FD must have super key.