The GATE Grind

GATE 2020 CS – Question 46

Databases · Integrity Constraints and Normal Forms · 2 marks · Multiple choice

Consider a relational table $R$ that is in 3NF, but not in BCNF. Which one of the following statements is TRUE?

  1. $R$ has a nontrivial functional dependency $X\to A$, where $X$ is not a superkey and $A$ is a prime attribute.
  2. $R$ has a nontrivial functional dependency $X\to A$, where $X$ is not a superkey and $A$ is a non-prime attribute and $X$ is not a proper subset of any key.
  3. $R$ has a nontrivial functional dependency $X\to A$, where $X$ is not a superkey and $A$ is a non-prime attribute and $X$ is a proper subset of some key.
  4. A cell in $R$ holds a set instead of an atomic value.

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Show answer and explanation

Correct answer: (A) $R$ has a nontrivial functional dependency $X\to A$, where $X$ is not a superkey and $A$ is a prime attribute.

Explanation

3NF requires that for every nontrivial FD $X\to A$, either $X$ is a superkey or $A$ is prime. Not being in BCNF means some FD has a non-superkey $X$, so $A$ must be prime.