Assuming the relation is in 1NF, if every non-key attribute is fully…

Concept

Database normal forms layer extra dependency restrictions on top of one another. The relevant principle here is partial dependency: a non-key (non-prime) attribute is partially dependent when it depends on only PART of a composite primary key rather than the whole key. The normal form whose defining rule is exactly "in 1NF and no partial dependency" is Second Normal Form.

Definitions, in increasing strictness:

• 1NF: all attribute values are atomic (no repeating groups or multivalued cells).

• 2NF: in 1NF AND every non-key attribute is fully functionally dependent on the WHOLE primary key (no partial dependency).

• 3NF: in 2NF AND no non-key attribute is transitively dependent on the primary key through another non-key attribute.

• 4NF: in BCNF AND for every non-trivial multivalued dependency X ->-> Y, the determinant X is a superkey.

Application to this statement

The stem gives two conditions: (1) the relation is already in 1NF, and (2) every non-key attribute is fully functionally dependent on the whole primary key. Condition (2) is precisely the statement "there is no partial dependency on a part of the composite key." Matching this against the definitions above, "1NF + full dependency on the whole key" is the exact defining rule of Second Normal Form, so the relation is in 2NF.

Cross-check / contrast

The stem says nothing about transitive dependencies, so we cannot claim 3NF: a relation can be fully dependent on the whole key yet still have one non-key attribute determining another (a transitive dependency), which would violate 3NF while still satisfying the given conditions. It also says nothing about multivalued dependencies, so 4NF is not implied. And 1NF alone only guarantees atomic values, which is weaker than the dependency condition stated. Hence the strongest form guaranteed by exactly these two conditions is 2NF.