Which one of the following statements if FALSE?

Answer: The false statement is: A prime attribute can be transitively dependent on a key in a BCNF relation.

Reasoning and brief checks of each statement:

• Any relation with two attributes is in BCNF: In a two-attribute relation, any nontrivial functional dependency makes the left attribute a key (it determines the other attribute). Therefore every determinant is a superkey and BCNF holds.

• A relation in which every key has only one attribute is in 2NF: 2NF eliminates partial dependencies on a part of a composite key. If no candidate key is composite (all keys are single-attribute), partial dependencies cannot exist, so the relation is in 2NF (assuming 1NF).

• A prime attribute can be transitively dependent on a key in a 3NF relation: 3NF allows a dependency X -> A when A is a prime attribute even if X is not a superkey. Thus a prime attribute may legitimately be reached transitively from a key and still satisfy 3NF.

• A prime attribute can be transitively dependent on a key in a BCNF relation: This is not allowed. BCNF requires every nontrivial determinant to be a superkey. A transitive chain key -> B -> primeAttribute includes the dependency B -> primeAttribute whose determinant B is not a superkey, so BCNF is violated.

Conclusion: The statement that a prime attribute can be transitively dependent on a key in a BCNF relation is false because BCNF forbids non-superkey determinants such as the intermediate attribute in a transitive dependency.