BCNF criterion — clarify the condition. "We have normalized a table into BCNF if all candidate keys are determinants."

Introduction / Context:
Boyce–Codd Normal Form (BCNF) strengthens Third Normal Form by eliminating anomalies from all functional dependencies (FDs). The statement given reverses the correct BCNF condition. Understanding the exact criterion is essential to avoid leaving non-key determinants that cause redundancy.

Given Data / Assumptions:

• Candidate keys are, by definition, determinants for all attributes in a relation.
• BCNF condition: for every nontrivial FD X -> Y, X must be a superkey.
• We are not discussing multivalued or join dependencies (handled by 4NF/5NF).

Concept / Approach:
Saying “all candidate keys are determinants” adds no information because keys always determine all attributes. The real question is whether any non-key determinant exists. If any FD has a left side that is not a superkey, the relation violates BCNF. Therefore, the statement is incorrect because it fails to rule out non-key determinants.

Step-by-Step Solution:

Verification / Alternative check:
Consider a relation with keys {A,B} and FDs B -> C. Even though {A,B} determines everything, B is a determinant but not a superkey, so the relation violates BCNF. This demonstrates why the statement is false.

Why Other Options Are Wrong:

• “Valid” misstates BCNF.
• Index presence or warehouse context is irrelevant to the logical condition.

Common Pitfalls:
Confusing “keys determine attributes” with the BCNF requirement; assuming 3NF equivalence; forgetting to test all FDs, not just those involving keys.

Final Answer:
Invalid (BCNF requires every determinant to be a superkey, not merely that keys are determinants)