In relational databases, if relation R is in BCNF, then which of the following…

Key idea: Boyce–Codd Normal Form (BCNF) requires that for every non-trivial functional dependency X → Y in a relation R, X must be a superkey (i.e., X functionally determines all attributes).

Consequences:

• Because every determinant is a superkey, there can be no partial dependencies on a part of a candidate key; this eliminates the kind of dependencies that violate 2NF.

• Similarly, BCNF prevents transitive dependencies of the form key → A and A → B where A is not a key, so it satisfies the requirements of 3NF.

• 1NF (atomic attribute values) is a baseline assumption; a relation in BCNF is taken to be in 1NF as well.

• BCNF does not necessarily imply 4NF, because 4NF addresses multivalued dependencies which are not eliminated solely by the BCNF requirement on functional dependencies.

Conclusion: If relation R is in BCNF, then R is in 2NF and 3NF (and typically in 1NF), but R is not guaranteed to be in 4NF.