A function that has no partial functional dependencies is in __________ form.

Concept

A partial functional dependency occurs when a non-prime attribute (an attribute not part of any candidate key) depends on only a proper subset of a candidate key, rather than on the whole key. Each normal form is defined by the specific kind of dependency anomaly it removes:

• 1NF removes repeating groups/non-atomic values.

• 2NF (1NF + no partial functional dependency of any non-prime attribute on a proper subset of a candidate key) removes partial dependencies.

• 3NF (2NF + for every functional dependency X -> A that holds, either X is a superkey or A is a prime attribute) removes transitive dependencies.

• BCNF strengthens 3NF by requiring every determinant of a functional dependency to be a superkey.

• 4NF (BCNF + every non-trivial multivalued dependency has a superkey as its determinant) removes multivalued-dependency anomalies.

Application

The blank in the stem asks for the normal form whose defining elimination criterion is exactly "no partial functional dependency." That criterion is, by definition, the boundary between 1NF and 2NF: a relation already in 1NF is promoted to 2NF precisely by removing every partial functional dependency of a non-prime attribute on a proper subset of a candidate key. So the blank is filled by 2NF.

Contrast

The other three normal forms are defined by a different elimination criterion, so none of them is a valid fit for this blank:

• 3NF's defining criterion is that every functional dependency X -> A must have X as a superkey or A as a prime attribute, eliminating transitive dependencies of a non-prime attribute through a non-superkey determinant, not partial dependencies.

• BCNF's defining criterion is that every determinant of any functional dependency must be a superkey — a condition about determinants, not about partial dependency on part of a key.

• 4NF's defining criterion is that every non-trivial multivalued dependency must have a superkey as its determinant, an entirely different (and stricter, later-stage) condition than partial functional dependency.

Note that 3NF, BCNF, and 4NF each additionally require the relation to already be free of partial dependencies (since they are progressively stronger than 2NF), but none of them is defined by that condition — 2NF is the unique form whose defining, distinguishing criterion is "no partial functional dependency."