Which of the following is TRUE?

Answer: Every relation in BCNF is also in 3NF.

BCNF condition: For every non-trivial functional dependency X -> A, X must be a superkey of the relation.

3NF condition: For every non-trivial functional dependency X -> A, either X is a superkey or A is a prime attribute (part of some candidate key).

Why BCNF implies 3NF: If every non-trivial dependency has a superkey on the left (BCNF), then the 3NF requirement is automatically met because one of 3NF's allowed conditions is that the left side is a superkey.

Why 3NF does not imply BCNF (counterexample): Consider a relation with attributes A, B, C and functional dependencies AB -> C and C -> B. The candidate keys are AB and AC, so every attribute is prime. The dependency C -> B has a non-superkey on the left, so BCNF is violated, but because B is a prime attribute the 3NF condition is satisfied. This shows a relation can be in 3NF but not in BCNF.

• Statement "Every relation in 3NF is also in BCNF": False. 3NF is weaker than BCNF; counterexamples exist.

• Statement "A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R": False. This describes 2NF/partial dependency ideas; 3NF uses the condition about superkeys or prime attributes.

• Statement "Every relation in BCNF is also in 3NF": True. BCNF's stronger requirement meets 3NF's conditions.

• Statement "No relation can be in both BCNF and 3NF": False. Relations can satisfy both; in fact any BCNF relation satisfies 3NF.