In a relational data model, which one of the following statements is TRUE?

Concept: Boyce–Codd Normal Form (BCNF) is a property of a relation schema. A relation is in BCNF if and only if, for every non-trivial functional dependency X -> Y that holds on it (with a non-empty determinant X, the standard convention here), the left side X is a superkey — that is, X determines all attributes of the relation.

Apply this to a relation R(A, B) that has exactly two attributes. Trace every non-trivial functional dependency that can exist on it:

1. With only two attributes, the only possible non-trivial dependencies are A -> B and B -> A.

2. If A -> B holds, then A also determines A trivially, so A determines both A and B; hence A is a superkey.

3. Symmetrically, if B -> A holds, then B determines both attributes, so B is a superkey.

4. If no non-trivial dependency holds at all, the BCNF condition is vacuously satisfied.

In every case the left side of any non-trivial dependency is a superkey, so the BCNF condition is never violated. Hence a relation with exactly two attributes is always in BCNF.

Cross-check against the other claims: a relation can be entirely composed of prime attributes and still break BCNF (e.g. R(A,B,C) with A -> B and B -> A but neither determining C, where candidate keys are AC and BC, so A,B,C are all prime yet A -> B has a non-superkey left side); a relation whose only candidate key is the full set of attributes has no non-prime attribute at all; and a BCNF decomposition guarantees a lossless join but not dependency preservation (e.g. R(A,B,C) with AB -> C and C -> B splits for BCNF into R1(B,C) and R2(A,C), which loses AB -> C — that preservation guarantee belongs to 3NF). So the two-attribute claim is the only universally true statement.