Question

Given that relation (R) has the following structure: R(A, B, C, D) with the following functional dependencies (FD): (A, B) → C and A → D.

a. What Normal Form does this relation violate?
b. Using the relational notation format above, modify the relation so that it is in Boyce-Codd Normal Form (BCNF).

Answer 1

The given relation violates BCNF. To modify it, the relation needs to be decomposed into two new relations: R1(A, B, C) and R2(A, D).

Step-by-step explanation:

In this case, the given relation violates the Boyce-Codd Normal Form (BCNF).

The BCNF violation occurs because there is a functional dependency (A, B) → C, where the determinant (A, B) is not a superkey for the relation.

To modify the relation to be in BCNF, we need to decompose it into two new relations: R1(A, B, C) and R2(A, D), where the primary keys of the new relations include the attributes that determine their non-key attributes.