In a relational schema R whenever a non-trivial functional dependency X-A holds in relation R, X is a super-key of relation R. Relation R is in _______.
The most suitable choice to fill in the blank is:

Question

In a relational schema R whenever a non-trivial functional dependency X->A holds in relation R, X is a super-key of relation R. Relation R is in _______. 
The most suitable choice to fill in the blank is:

Accepted Answer

The correct option is (1):
The statement provided, "whenever a non-trivial functional dependency X-\>A holds in relation R, X is a super-key of relation R," is the formal, defining condition for Boyce-Codd Normal Form (BCNF). BCNF is considered a stricter version of Third Normal Form (3NF). In BCNF, we essentially require that the left side of *every* non-trivial functional dependency, which is called the determinant, must be a superkey. The rationale behind this is to ensure that the redundancy caused by functional dependencies is completely eliminated, thereby preventing insertion, deletion, and update anomalies in the database schema. If a relation satisfies this rule, it is guaranteed to be free of all functional dependency-based anomalies, which is why database designers often aim for BCNF.

The incorrect option is (2):
Second Normal Form (2NF) is an insufficient condition for the given definition. 2NF focuses on eliminating partial dependencies, meaning every non-key attribute must be fully functionally dependent on the entire primary key. The question's condition is much broader and stricter: it mandates that *any* determinant of a non-trivial functional dependency must be a superkey, regardless of whether the attribute being determined is key or non-key. For instance, a relation can satisfy 2NF but still violate BCNF in certain complex scenarios involving overlapping candidate keys. Therefore, a relation meeting the BCNF definition automatically meets 2NF, but not vice-versa.

The incorrect option is (3):
Third Normal Form (3NF) is also not the most suitable choice, as BCNF is a stronger criterion than 3NF. 3NF eliminates transitive dependencies, requiring that non-prime attributes do not depend on other non-prime attributes. A relation can be in 3NF but fail to be in BCNF, typically when the relation has multiple overlapping candidate keys where a non-key attribute determines a key attribute. The precise definition provided in the question—where every determinant is a superkey—is what differentiates BCNF from 3NF, making BCNF the correct identifier for this rule.

The incorrect option is (4):
Fourth Normal Form (4NF) is a higher level of normalization that is concerned with a different type of dependency known as Multi-Valued Dependency (MVD). 4NF states that a relation must be in BCNF and have no non-trivial MVDs. Since the question is exclusively framed in terms of functional dependencies (X-\>A) and the condition is the exact definition of BCNF, introducing MVDs unnecessarily makes 4NF too strict for this specific definition. The condition provided is the rule for BCNF, not 4NF.