Relation R is decomposed using a set of functional dependencies, F and…
2002
Relation R is decomposed using a set of functional dependencies, F and relation S is decomposed using another set of functional dependencies G. One decomposition is definitely BCNF, the other is definitely 3NF, but it is not known which is which. To make a guaranteed identification, which one of the following tests should be used on the decompositions? (Assume that the closures of F and G are available).
- A.
Dependency-preservation
- B.
Lossless-join
- C.
BCNF definition
- D.
3NF definition
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Correct answer: C
To identify which decomposition is BCNF and which is 3NF, the BCNF definition must be checked. BCNF requires that for every functional dependency X→Y, X must be a superkey. This is a strict condition that only BCNF satisfies.
3NF is a weaker normal form that allows some non-superkey determinants under specific conditions. Therefore, checking the 3NF definition would not distinguish between the two, as both decompositions could satisfy 3NF.
Dependency-preservation and lossless-join are properties that both BCNF and 3NF decompositions can have, so they cannot be used to distinguish between the two normal forms.
Thus, the only reliable test is to verify the BCNF definition on each decomposed relation.
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