GATE CS 2019 Set 1 — Question 42
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Databases → Normalization → BCNF
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Question
Let the set of functional dependencies hold on a relation schema . is not in BCNF. Suppose is decomposed into two schemas and , where and .Consider the two statements given below.I. Both and are in BCNF
II. Decomposition of into and is dependency preserving and losslessWhich of the above statements is/are correct?
II. Decomposition of into and is dependency preserving and losslessWhich of the above statements is/are correct?
Correct answer
(C) II only
Solution
First, find the candidate keys for
X(PQRS) with .- (via
R → P). So is a key. - . So is a key.
- For
Y(PR): The FD isR → P. Since is the key for , is in BCNF. - For
Z(QRS): The FDs areQR → SandS → Q. The keys for are and . The dependencyS → Qholds in , but is not a superkey of . Thus, is not in BCNF. - Therefore, Statement I is False.
- Lossless Join: . Since
R → Pholds, is a key forY(PR). The intersection is a superkey of one of the relations, so the decomposition is lossless. - Dependency Preserving:
R → Pis preserved in .QR → SandS → Qare preserved in .- All dependencies in are preserved.
- Therefore, Statement II is True.
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