GATE 2022

Question 14

In a relational data model, which one of the following statements is TRUE?

A	A relation with only two attributes is always in BCNF.
B	If all attributes of a relation are prime attributes, then the relation is in BCNF.
C	Every relation has at least one non-prime attribute.
D	BCNF decompositions preserve functional dependencies.

Database-Management-SystemNormalizationVideo-Explanation

Question 14 Explanation:

A relation with only two attributes will always be in BCNF.
Example:
R(A, B).
Two functional dependencies possible for the relation: (1) A->B and (2) B->A
If there is no functional dependency, we can assume trivial functional dependencies like AB->A and AB->B.
In all cases, functional dependencies like A->B, A must be a key.
So they all will be in BCNF irrespective of the functional depencies set.

Correct Answer: A

Question 14 Explanation:

A relation with only two attributes will always be in BCNF.
Example:
R(A, B).
Two functional dependencies possible for the relation: (1) A->B and (2) B->A
If there is no functional dependency, we can assume trivial functional dependencies like AB->A and AB->B.
In all cases, functional dependencies like A->B, A must be a key.
So they all will be in BCNF irrespective of the functional depencies set.