Relation R with an associated set of functional dependencies, F is decomposed…

2002

Relation R with an associated set of functional dependencies, F is decomposed into BCNF. The redundancy (arising out of functional dependencies) in the resulting set relations is.

  1. A.

    Zero

  2. B.

    More than zero but less than that of an equivalent 3NF decomposition

  3. C.

    Proportional to the size of F⁺

  4. D.

    Indeterminate

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Correct answer: A

Answer: Zero.

Why: By definition, a relation in Boyce–Codd Normal Form (BCNF) has the property that for every nontrivial functional dependency X → Y that holds in the relation, X is a superkey. Because no nonkey-based functional dependencies remain, there are no functional dependencies that force repeated values of nonkey attributes within a relation. Thus redundancy caused by the functional dependencies is eliminated.

  • BCNF removes FD-based redundancy within each decomposed relation because every determinant is a key.

  • Note: BCNF decompositions are lossless, so they do not introduce spurious tuples, but they may not always preserve all original functional dependencies. That preservation issue does not change the fact that redundancy arising from satisfied functional dependencies is zero in the BCNF relations.

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