Consider a schema R(MNPQ) and functional dependencies M → N, P → Q. Then the…
2017
Consider a schema R(MNPQ) and functional dependencies M → N, P → Q. Then the decomposition of R into R1 (MN) and R2 (PQ) is ________.
- A.
Dependency preserving but not lossless join
- B.
Dependency preserving and lossless join
- C.
Lossless join but not dependency preserving
- D.
Neither dependency preserving nor lossless join.
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Correct answer: A
Answer: Dependency preserving but not lossless join
Reason: Check dependency preservation and lossless-join separately.
Dependency preservation: The functional dependency M → N is entirely contained in R1(M, N), and P → Q is entirely contained in R2(P, Q). Because each given dependency applies within one of the decomposed relations, all original dependencies are preserved.
Lossless-join test: The intersection of R1 and R2 is empty (R1 ∩ R2 = ∅), so there are no common attributes. For a decomposition of R into R1 and R2 to be lossless, the intersection must functionally determine one of the relations using the given FDs. Here the empty set does not determine any attributes under the given FDs, so the lossless condition is not satisfied.
Conclusion: The decomposition preserves dependencies but is not lossless.
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