October 16, 2023
October 16, 2023
October 16, 2023
###### GATE 2022
October 16, 2023
 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.
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.
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.