Question

Given a relation R(A,B,C,D). Which of the followings is trivial?

Select one:
a. A->->BCD
b. A->AB
c. A->BCD
d. A->->AB

Answer 1

Option b. A->AB is a trivial functional dependency because attribute B, on the right side, is included in the set of attributes on the left side of the dependency, conforming to the axiom of reflexivity.

Step-by-step explanation:

The relation R(A,B,C,D) is given, and we need to determine which of the following is trivial:

• A->AB
• A->BCD
• A->->AB
• A->->BCD

In database terms, a trivial functional dependency means that the dependency can be derived from the basic axioms of functional dependencies, particularly the axiom of reflexivity which states that if X is a set of attributes and Y is a subset of X, then X determines Y. Thus, a functional dependency is trivial if the right side is a subset of the left side.

Looking at the options given, we can see that option b. A->AB is trivial. This is because B is a subset of AB, which includes attribute A as specified on the left side of the dependency.