A relation is in which normal form if it is in Boyce–Codd normal form and also has no multivalued dependencies?

Introduction / Context:
Normalization levels build on one another. Beyond Boyce–Codd normal form, the next target addresses multivalued dependencies explicitly.

Given Data / Assumptions:

• The relation already satisfies Boyce–Codd normal form.
• We now eliminate nontrivial multivalued dependencies.

Concept / Approach:
Fourth normal form is achieved when a relation is in Boyce–Codd normal form and contains no nontrivial multivalued dependencies. This ensures that attributes do not vary independently in a way that causes redundancy.

Step-by-Step Solution:

Verification / Alternative check:
After decomposition, updates to one attribute set need not cascade to another, validating the removal of multivalued dependency anomalies.

Why Other Options Are Wrong:

• Second and third normal forms are weaker and do not mention multivalued dependencies.
• Domain/key normal form is stricter than fourth and is not required merely by BCNF plus removal of multivalued dependencies.

Common Pitfalls:
Assuming BCNF alone handles multivalued dependencies. It does not; fourth normal form is required.

Final Answer:
fourth normal form.