GATE DA 2025 Set 1 — Question 57
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Database Management & Warehousing → Normalization → BCNF
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Question
Consider a database relation R with attributes ABCDEFG, and having the following functional dependencies:Which of the following statements is/are correct?
Correct answer
(B) A, BC are the candidate keys of R; (D) Relation R is not in Boyce-Codd Normal Form (BCNF)
Solution
1.Find candidate keys:
- Closure of : . From , we get . So . is a candidate key.
- Closure of :
BC → A, and since is a key, is also a key. - Closure of :
E → D, G. . Not a key. - No other subset determines all attributes. Candidate keys are .
- A relation is in BCNF if for every non-trivial dependency
X → Y, is a superkey. - Dependency
E → DG: is not a superkey. This violates BCNF.
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