GATE 2022
October 16, 2023GATE 2022
October 16, 2023GATE 2022
Question 14

In a relational data model, which one of the following statements is TRUE?
A relation with only two attributes is always in BCNF.


If all attributes of a relation are prime attributes, then the relation is in BCNF.


Every relation has at least one nonprime attribute.


BCNF decompositions preserve functional dependencies.

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.
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.
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.
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