Consider a relational table $R$ that is in 3NF, but not in BCNF. Which one of the following statements is TRUE?

A relation $R$ is in 3NF if for every non-trivial functional dependency $X \rightarrow A$:

1. $X$ is a superkey, OR

2. $A$ is a prime attribute (i.e., part of some candidate key).

A relation $R$ is in BCNF if for every non-trivial functional dependency $X \rightarrow A$, $X$ is a superkey.

Therefore, for a relation $R$ to be in 3NF but not in BCNF, there must exist at least one non-trivial functional dependency $X \rightarrow A$ where $X$ is not a superkey, while $A$ is a prime attribute.

• (A) is TRUE as it directly describes the condition under which 3NF holds while BCNF is violated.

• (B) describes a transitive dependency involving a non-prime attribute, which violates 3NF.

• (C) describes a partial dependency, which violates 2NF.

• (D) describes non-atomic attributes, which violates 1NF.