Which one of the following statements about normal forms is FALSE ?
2015
Which one of the following statements about normal forms is FALSE ?
- A.
Lossless, dependency-preserving decomposition into 3NF is always possible
- B.
Lossless, dependency-preserving decomposition into BCNF is always possible
- C.
Any relation with two attributes is in BCNF
- D.
BCNF is stricter than 3NF
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Correct answer: B
Correct answer: Lossless, dependency-preserving decomposition into BCNF is always possible.
Why this is false: Decomposing a relation into BCNF can ensure a lossless decomposition, but it does not always preserve all original functional dependencies. Some relations require breaking dependencies to achieve BCNF, so a decomposition that is both lossless and dependency-preserving into BCNF is not guaranteed.
Why the 3NF statement is true: The standard 3NF synthesis algorithm (using a minimal cover of the functional dependencies) produces a decomposition that is both lossless and dependency-preserving.
Why any two-attribute relation is in BCNF: With only two attributes A and B, any nontrivial dependency (A -> B or B -> A) makes the determinant a key, satisfying BCNF.
Why BCNF is stricter than 3NF: BCNF requires every nontrivial functional dependency to have a superkey as determinant. 3NF relaxes this by allowing dependencies where the dependent is a prime attribute, so BCNF imposes a stronger condition.