A relation in which every non-key attribute is fully functionally dependant on the primary key and which has no transitive dependencies is said to be in:

Question

Accepted Answer

The correct option is (3):
A relation is in the Third Normal Form (3NF) if and only if it satisfies two main conditions: first, it must be in 2NF, and second, no non-key attribute is transitively dependent on the primary key. The question explicitly combines these two fundamental requirements. The phrase "every non-key attribute is fully functionally dependant on the primary key" is the core definition of a relation being in 2NF, ensuring the elimination of partial dependencies. The second phrase, "which has no transitive dependencies," is the specific, additional criterion that elevates a 2NF relation to 3NF. Transitive dependency exists when a non-key attribute is functionally dependent on another non-key attribute, which, in turn, is dependent on the primary key. Eliminating this type of redundancy is the key objective of 3NF, as it significantly improves data integrity and prevents many common types of update, insertion, and deletion anomalies.

The incorrect option is (1):
The Boyce-Codd Normal Form (BCNF) is a stricter and more rigorous version of 3NF. While a relation in BCNF is always in 3NF, the reverse is not always true. BCNF’s definition requires that for every non-trivial functional dependency ($X \rightarrow Y$), the determinant $X$ must be a superkey. This addresses certain complex anomalies involving overlapping candidate keys, which 3NF does not explicitly cover. Since the provided definition perfectly and completely describes the criteria for 3NF (full dependency on the primary key AND no transitive dependency) without adding the extra conditions BCNF is designed to resolve, 3NF is the more precise answer.

The incorrect option is (2):
The Second Normal Form (2NF) is a less restrictive condition than 3NF. A relation is in 2NF if it is in 1NF and every non-key attribute is fully functionally dependent on the entire primary key, thereby eliminating partial dependencies. However, the definition of 2NF does *not* require the elimination of transitive dependencies. A relation can be in 2NF and still contain transitive dependencies, which would allow for various data anomalies. Since the question explicitly states that the relation "has no transitive dependencies," it is describing a higher, more normalized state than 2NF.

The incorrect option is (4):
The Fourth Normal Form (4NF) is concerned with dependencies that go beyond simple functional dependencies. A relation is in 4NF if it is in BCNF and contains no non-trivial multi-valued dependencies (MVDs). MVDs occur when a determinant determines multiple independent sets of values, a more complex scenario not covered by the functional and transitive dependencies mentioned in the question. Since the question is framed purely in terms of removing partial and transitive *functional* dependencies, 4NF is an irrelevant and overly strict normal form for the given definition.