Consider the table R with attributes A, B and C. The functional dependencies…
2016
Consider the table R with attributes A, B and C. The functional dependencies that hold on
R are : A → B, C → AB. Which of the following statements is/are True ?
I. The decomposition of R into R1(C, A) and R2(A, B) is lossless.
II. The decomposition of R into R1(A, B) and R2(B, C) is lossy.
- A.
Only I
- B.
Only II
- C.
Both I and II
- D.
Neither I nor II
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Correct answer: C
Answer: Both I and II are true.
Reasoning:
First decomposition into {C, A} and {A, B}: the intersection is {A}. Using the functional dependency A → B, compute A+ = {A, B}. Since A+ contains all attributes of the relation {A, B}, the intersection functionally determines one of the decomposed relations, so the decomposition is lossless.
Second decomposition into {A, B} and {B, C}: the intersection is {B}. Compute B+ using the given dependencies: no FD has B on the left, so B+ = {B}. Because B does not determine either {A, B} or {B, C}, the lossless-join condition fails and the decomposition is lossy.
Therefore both statements I and II are true.
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