Consider the schema R(A, B, C, D) and the functional dependencies A->B and…
2014
Consider the schema R(A, B, C, D) and the functional dependencies A->B and C->D. If the decomposition is made as R1(A,B) and R2(C,D), then which of the following is TRUE?
- A.
Preserves dependency but cannot perform lossless join
- B.
Preserves dependency and performs lossless join
- C.
Does not perform dependency and cannot perform lossless join
- D.
Does not preserve dependency but perform lossless join
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Correct answer: A
The functional dependencies A→B and C→D are fully contained within R1(A,B) and R2(C,D), ensuring dependency preservation. However, the intersection of attributes between R1 and R2 is empty. For a lossless join, the intersection must functionally determine at least one relation. Since there are no common attributes, this condition is not met, and the decomposition is not lossless.