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

Let us evaluate each of the given options:

• (A) is TRUE: Consider any relation $R(A, B)$ with two attributes. The only possible non-trivial functional dependencies are $A \to B$, $B \to A$, or both. In any non-trivial dependency (such as $A \to B$), the determinant $A$ is a candidate key (and thus a superkey). If there are no non-trivial dependencies, the key is $AB$. In all cases, every non-trivial FD $X \to Y$ has $X$ as a superkey. Therefore, any two-attribute relation is always in BCNF.

• (B) is FALSE: If all attributes are prime, the relation is guaranteed to be in 3NF, but not necessarily in BCNF. For example, in $R(A, B, C)$ with FDs $AB \to C$ and $C \to B$, candidate keys are $AB$ and $AC$. All attributes $\{A, B, C\}$ are prime, but $C \to B$ violates BCNF because $C$ is not a superkey.

• (C) is FALSE: An all-key relation consists solely of prime attributes and has zero non-prime attributes.

• (D) is FALSE: BCNF decomposition is always lossless, but it is not always dependency-preserving.

Hence, option (A) is the correct answer.