R(A,B,C,D) is a relation. Which of the following does not have a lossless…
2001
R(A,B,C,D) is a relation. Which of the following does not have a lossless join, dependency preserving BCNF decomposition?
Answer: C. AB->C, C->AD — we have, R(A, B, C, D) and the Functional Dependency set = {AB→C, C→AD}. we decompose it as R1(A, B, C) and R2(C, D). This preserves all dependencies and the…
- A.
A->B, B->CD
- B.
A->B, B->C, C->D
- C.
AB->C, C->AD
- D.
A ->BCD
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Correct answer: C
we have, R(A, B, C, D) and the Functional Dependency set = {AB→C, C→AD}.
we decompose it as R1(A, B, C) and R2(C, D). This preserves all dependencies and the join is lossless too, but the relation R1 is not in BCNF. In R1 we keep ABC together otherwise preserving {AB→C} will fail, but doing so also causes {C→A} to appear in R1. {C→A} violates the condition for R1 to be in BCNF as C is not a superkey. Condition that all relations formed after decomposition should be in BCNF is not satisfied here.
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