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GATE | GATE CS 2020 | Question 46

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

(A)

R has a nontrivial functional dependency X→A, where X is not a superkey and A is a prime attribute

(B)

R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is not a proper subset of any key

(C)

R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is a proper subset of some key

(D)

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


Answer: (A)

Explanation:

A relation is in 3NF if at least one of the following condition holds in every non-trivial function dependency X → Y:

  1. X is a super key. (This condition is must for BCNF relations.).
  2. Y is a prime attribute (each element of Y is part of some candidate key).

But, a relation is in BCNF if, X is superkey for every functional dependency (FD) X → Y in given relation.

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Therefore, BCNF relations are subset of 3NF relations. Means every BCNF relation is 3NF but converse may not true. 

Option (A) is correct.


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Last Updated : 26 May, 2021
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