A relation is in which normal form if it is in Boyce–Codd normal form and also has no multivalued dependencies?
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Asecond normal form.
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Bthird normal form.
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Cfourth normal form.
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Ddomain/key normal form.
Answer
Correct Answer: fourth normal form.
Explanation
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:
Confirm BCNF holds (determinants are candidate keys).Check for multivalued dependencies; if present, decompose appropriately.Once none remain, the relation is in fourth normal form.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.