GATE 2026 CS (CS1) – Question 31
In the context of relational database normalization, which of the following statements is/are true?
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Correct answer: (A) It is always possible to obtain a dependency-preserving 3NF decomposition of a relation; (B) It is always possible to obtain a dependency-preserving 1NF decomposition of a relation; (C) It is not always possible to obtain a dependency-preserving BCNF decomposition of a relation
Explanation
- (A) is true: The 3NF synthesis algorithm (Bernstein's algorithm) is mathematically guaranteed to produce a lossless-join and dependency-preserving 3NF decomposition for any relational schema and set of functional dependencies.
- (B) is true: 1NF requires only atomic domains, which does not decompose relations or split functional dependencies, thus preserving all dependencies trivially.
- (C) is true: While a lossless-join BCNF decomposition is always achievable, dependency preservation is NOT always possible in BCNF (classic counterexample: $R(A, B, C)$ with $AB \to C$ and $C \to B$).
- (D) is false: Since 3NF is strictly stronger than 2NF and a dependency-preserving 3NF decomposition is always possible, a dependency-preserving 2NF decomposition is also always possible.
Therefore, statements (A), (B), and (C) are true.