GATE CS 2020 Set 1 — Question 46
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Databases → Normalization → 1NF, 2NF, 3NF
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Question
Consider a relational table that is in 3NF, but not in BCNF. Which one of the following statements is TRUE?
Correct answer
(A) R has a nontrivial functional dependency X → A, where X is not a superkey and A is a prime attribute.
Solution
Definitions:
If is in 3NF but not in BCNF, there must exist at least one dependency
- 3NF: A relation is in 3NF if for every non-trivial functional dependency
X → A, either is a superkey OR is a prime attribute (part of some candidate key). - BCNF: A relation is in BCNF if for every non-trivial functional dependency
X → A, is a superkey.
If is in 3NF but not in BCNF, there must exist at least one dependency
X → A that satisfies the 3NF condition but violates the BCNF condition.- Violates BCNF: is not a superkey.
- Satisfies 3NF: Since is not a superkey, the only way to satisfy 3NF is if is a prime attribute.
X → A where is not a superkey and is a prime attribute.Option (A) states exactly this condition.Continue learning with Success Tracker
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