Given a relation R(A,B,C,D) with FDs A→B, C→D, and a decomposition into…
Given a relation R(A,B,C,D) with FDs A→B, C→D, and a decomposition into R1(A,B) and R2(C,D), which statement is true?
Answer: A. The decomposition is dependency preserving. — Dependency Preserving: FD A→B is preserved in R1(A,B). FD C→D is preserved in R2(C,D). Lossless Join: For a decomposition to be lossless, the intersection of…
- A.
The decomposition is dependency preserving.
- B.
The decomposition is lossless.
- C.
The decomposition is neither dependency preserving nor lossless.
- D.
The decomposition is both dependency preserving and lossless.
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Correct answer: A
Dependency Preserving:
FD A→B is preserved in R1(A,B).
FD C→D is preserved in R2(C,D).
Lossless Join:
For a decomposition to be lossless, the intersection of the decomposed relations must form a superkey in at least one of the original relations.
R1 and R2 have no common attributes, so R1∩R2=∅, which does not form a superkey.