Which of the following is TRUE? A) Every relation in 3NF is also in BCNF B) A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R C) Every relation in BCNF is also in 3NF D) No relation can be in both BCNF and 3NF

Official answer: C) Every relation in BCNF is also in 3NF. Explanation: Normal forms have a strict hierarchical relationship with respect to normalization strength: 4NF ⊂ BCNF ⊂ 3NF ⊂ 2NF ⊂ 1NF - Option (A) is false: Not every relation in 3NF is in BCNF (BCNF is stricter than 3NF). - Option (B) is false: This describes 2NF (no partial dependencies of non-prime attributes on candidate keys), not 3NF (which additionally requires no transitive dependencies). - Option (C) is true: Every relation in BCNF is also in 3NF because BCNF is a stronger normal form. - Option (D) is false: Any relation that is in BCNF is also in 3NF. Hence, the correct option is (C).

A) Every relation in 3NF is also in BCNF

B) A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R

D) No relation can be in both BCNF and 3NF

Integrity Constraints and Normal Forms

GATE CSE 2012 · Q2

MCQ1 markEasy

Time00:00

Which of the following is $\textbf{TRUE}$ ?

Select one answerSingle correct

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Solution

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Official answer: C) Every relation in BCNF is also in 3NF

Integrity Constraints and Normal Forms

Normal forms have a strict hierarchical relationship with respect to normalization strength:

\text{4NF} \subset \text{BCNF} \subset \text{3NF} \subset \text{2NF} \subset \text{1NF}

Option (A) is false: Not every relation in 3NF is in BCNF (BCNF is stricter than 3NF).
Option (B) is false: This describes 2NF (no partial dependencies of non-prime attributes on candidate keys), not 3NF (which additionally requires no transitive dependencies).
Option (C) is true: Every relation in BCNF is also in 3NF because BCNF is a stronger normal form.
Option (D) is false: Any relation that is in BCNF is also in 3NF.

Hence, the correct option is (C).

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This Integrity Constraints and Normal Forms previous year question is Q2 of the GATE CSE 2012 paper. Find more GATE CSE PYQs on Integrity Constraints and Normal Forms in Databases, or browse all GATE CSE PYQs.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.