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GATE CSE 2026 | Set 1 | Question: 21

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

  1. It is always possible to obtain a dependency-preserving $3$NF decomposition of a relation
  2. It is always possible to obtain a dependency-preserving $1$NF decomposition of a relation
  3. It is not always possible to obtain a dependency-preserving BCNF decomposition of a relation
  4. It is not always possible to obtain a dependency-preserving $2$NF decomposition of a relation

3 Answers

2 2 votes

Answer: A, B,C

It is always possible to obtain a dependency-preserving 3 NF decomposition of a relation but not for BCNF.

Proof:

As every 3NF is in 2NF and every 2NF is in 1NF:

  1. It is always possible to obtain a dependency-preserving 1 NF decomposition of a relation
  2. It is always possible to obtain a dependency-preserving 2 NF decomposition of a relation $\Rightarrow$ Option D is wrong.
0 0 votes

1. In 3NF decomposition of a relation, we'll always obtain both Lossless Decompostion and Dependency-Preserving.

2. But in BCNF decomposition of a relation, we'll always obtain Lossless Decompostion but we may or may not obtain Dependency Preserving.

So, as per the above two statements, the correct options are A, B and C.

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