GATE CS 2026 Set 1 Q.31: Functional Dependencies and Normalization

In the context of relational database normalization, which of the following statements is/are true?

It is always possible to obtain a dependency-preserving 3NF decomposition of a relation

It is always possible to obtain a dependency-preserving 1NF decomposition of a relation

It is not always possible to obtain a dependency-preserving BCNF decomposition of a relation

It is not always possible to obtain a dependency-preserving 2NF decomposition of a relation

Official answer and solution

Official answer: A, B and C
From: Official GATE 2026 answer key

Solution

Use the standard theorem that every relational schema admits a lossless-join, dependency-preserving 3NF synthesis (which is also in 2NF and 1NF), whereas BCNF does not always preserve dependencies.

Option (A) is true: Using the canonical cover synthesis algorithm, it is always possible to obtain a lossless-join and dependency-preserving 3NF decomposition of any relation.
Option (B) is true and Option (D) is false: Since every relation in 3NF is also in 2NF and 1NF, a dependency-preserving 3NF decomposition is automatically a dependency-preserving 2NF and 1NF decomposition.
Option (C) is true: There exist relational schemas (such as $R(A, B, C)$ with $AB \rightarrow C$ and $C \rightarrow B$ ) for which no BCNF decomposition is dependency-preserving.

Final answer

Options (A), (B), (C)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
Question: 31 of 65
Section: Computer Science and Information Technology

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