GATE CS 2020 Q.46 (CS Q.36): Functional Dependencies and Normalization

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

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

$R$ 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.

$R$ 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.

A cell in $R$ holds a set instead of an atomic value.

Official answer and solution

Official answer: A
From: Official GATE 2020 answer key

Solution

Compare the definitions of Third Normal Form (3NF) and Boyce-Codd Normal Form (BCNF).

Definitions:

For a relation $R$ to be in BCNF, for every non-trivial functional dependency $X \to A$ , $X$ must be a superkey of $R$ .
For a relation $R$ $R$ to be in 3NF, for every non-trivial functional dependency $X \to A$ $X \to A$ , either:
1. $X$ is a superkey of $R$ , OR
2. $A$ is a prime attribute (an attribute that is part of some candidate key of $R$ ).

Condition for being in 3NF but not in BCNF:

Since $R$ is not in BCNF, there exists at least one non-trivial functional dependency $X \to A$ where $X$ is NOT a superkey.
However, because $R$ is in 3NF, this functional dependency must satisfy condition (2) of 3NF. Thus, $A$ MUST be a prime attribute.
Therefore, $R$ must have a non-trivial functional dependency $X \to A$ where $X$ is not a superkey and $A$ is a prime attribute.

Final answer

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

Source

Paper: GATE 2020 Computer Science and Information Technology (CS)
Question: 46 of 65, printed as CS Q.36
Section: Computer Science and Information Technology

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source