In BCNF, what defines a determinant?

• A. A determinant is a set of attributes on which a non-trivial functional dependency rests; in BCNF, determinants must be candidate keys.
• B. A determinant is a foreign key.
• C. A determinant is a derived attribute.
• D. A determinant is any attribute that determines the whole relation.

Answer: (A)

In BCNF, a determinant is the set of attributes on the left-hand side of a non-trivial functional dependency—the attributes that determine the values of other attributes. The idea is that for any non-trivial dependency X -> Y, X should be a key for the relation, so every determinant must functionally determine all attributes, making it a (candidate) key.

This is why the best answer states that a determinant is a set of attributes on which a non-trivial functional dependency rests, and in BCNF, determinants must be candidate keys. It aligns with the BCNF requirement that the left-hand side of every non-trivial dependency be a key.

Why the other choices don’t fit: a foreign key is about linking to a row in another relation, not about determining attributes within the same relation; a derived attribute is computed from other attributes and not about the left-hand side of a functional dependency; and saying any attribute that determines the whole relation is too narrow and ignores that a determinant can be a set of attributes (and BCNF emphasizes the left-hand side being a key).