Relation: x=(d,b,c,f,g,h) Functional dependencies: d→bc,g→hd Decomposed into:…
Relation: x=(d,b,c,f,g,h)
Functional dependencies: d→bc,g→hd
Decomposed into:
a=(d,b,c)
e=(d,f,g,h)
Which of the following is correct?
Answer: B. Lossless and dependency preservation — Step 1: Check Dependency Preservation Given FDs: d→bc Decomposition: Relation a(d,b,c): Can enforce d→bc. Relation e(d,f,g,h): Can enforce g→hd. Since both…
- A.
Lossy and dependency preservation
- B.
Lossless and dependency preservation
- C.
Lossless and no dependency preservation
- D.
Lossy and not dependency preservation
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Correct answer: B
Step 1: Check Dependency Preservation
Given FDs: d→bc
Decomposition:
Relation a(d,b,c): Can enforce d→bc.
Relation e(d,f,g,h): Can enforce g→hd.
Since both FDs can be enforced in their respective relations, the decomposition preserves dependencies.
Step 2: Check Lossless Join
A decomposition is lossless if the common attributes between relations form a superkey in at least one of the decomposed relations.
Common attribute: d.
d is a superkey in a (because d→bc).
Thus, the decomposition is lossless.