Which of the following best describes Fourth Normal Form (4NF)?

Question

BlackTom AI · Accepted Answer

Fourth Normal Form (4NF) requires that every nontrivial multi-valued dependency (MVD) X ->> Y in a relation has X as a superkey. In other words, 4NF eliminates undesirable multi-valued dependencies that can cause redundancy beyond what functional dependency–based normal forms (like 3NF/BCNF) address.

1. Relevant knowledge points and concepts
- 1NF: atomic (no repeating groups).
- 2NF: no partial dependencies (applies to relations with composite keys).
- 3NF: no transitive dependencies with respect to functional dependencies (FDs).
- BCNF: every nontrivial FD has a superkey as determinant (stricter FD condition).
- MVD (X ->> Y): presence of independent multi-valued attributes; MVDs are a different class of dependency than FDs.
- 4NF: for every nontrivial MVD X ->> Y, X must be a superkey (equivalently, the relation has no nontrivial MVDs unless the determinant is a superkey).

2. Step-by-step reasoning
- 3NF (or BCNF) handles redundancies caused by functional dependencies, but functional-dependency normalization does not remove redundancies caused by multi-valued dependencies.
- If a relation is in 3NF but still has a nontrivial MVD A ->> B where A is not a superkey, then multiple independent B-values per A will create redundancy; 4NF requires removing such MVDs by decomposition.
- Therefore, a relation that is in 3NF and has no nontrivial MVDs meets the 4NF requirement.

3. Intermediate demonstration (example)
- R(Student, Course, Hobby) with Student ->> Course and Student ->> Hobby (Student is not a superkey): redundancy exists.
- Decompose into R1(Student, Course) and R2(Student, Hobby) to eliminate MVDs and achieve 4NF.

4. Why the correct answer is correct
- The option "A relation that has no multi-valued dependencies and is in 3NF" states both that FD-related issues (3NF) are resolved and that no MVDs remain. This satisfies the 4NF condition that there be no nontrivial MVDs unless the determinant is a superkey.

5. Why the other options are incorrect
- "No partial dependencies": describes 2NF, not 4NF.
- "No transitive dependencies": describes 3NF, not 4NF.
- "Only atomic attributes and in BCNF": atomic attributes = 1NF; BCNF addresses FDs but does not guarantee elimination of MVDs, so BCNF alone may still violate 4NF.

6. Conclusion
The correct description of 4NF is: "A relation that has no multi-valued dependencies and is in 3NF." This matches the provided answer.

Which of the following best describes Fourth Normal Form (4NF)?单项选择题

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