BCNF criterion — evaluate the statement: “A relation is in Boyce–Codd Normal Form (BCNF) if every determinant is a composite key.” Determine whether this is correct or incorrect.

Introduction / Context: Boyce–Codd Normal Form (BCNF) strengthens Third Normal Form by tightening the condition on determinants (the left-hand sides of functional dependencies). Understanding the exact requirement avoids incorrect schema validations.

Given Data / Assumptions:

• Determinant means the attribute set on the left side of an FD X → Y.
• Candidate key means a minimal superkey — it functionally determines all attributes of the relation.
• Keys can be single-attribute or composite.

Concept / Approach: The BCNF condition is: for every nontrivial FD X → Y that holds in the relation, X must be a superkey (equivalently, every determinant is a candidate key when minimal). There is no requirement that X be composite; a single-attribute key satisfies BCNF just as well. Therefore, saying “every determinant is a composite key” is too restrictive and incorrect.

Step-by-Step Solution:

Verification / Alternative check: Example: Relation R(A, B, C) with key A (single attribute). If the only FDs are A → B, A → C, then X = A is a determinant and a candidate key; R is in BCNF even though the determinant is not composite.

Why Other Options Are Wrong:

• “Correct — determinants must be composite” contradicts the definition.
• Dependence on FD count or absence of single-attribute keys is irrelevant.
• BCNF is unrelated to foreign keys specifically.

Common Pitfalls: Confusing “stronger than 3NF” with “requires composite keys”; thinking BCNF forbids single-attribute keys.

Final Answer: Incorrect — BCNF requires every determinant to be a candidate key (composite or single-attribute)