The GATE Grind

GATE 2025 DA – Question 57

Database Management and Warehousing · Integrity constraints and normal forms · 2 marks · Multiple select

Consider a database relation R with attributes ABCDEFG, and having the following functional dependencies:

$A \to BCEF$

$E \to DG$

$BC \to A$

Which of the following statements is/are correct?

  1. A is the only candidate key of R
  2. A, BC are the candidate keys of R
  3. A, BC, E are the candidate keys of R
  4. Relation R is not in Boyce-Codd Normal Form (BCNF)

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Correct answer: (B) A, BC are the candidate keys of R; (D) Relation R is not in Boyce-Codd Normal Form (BCNF)

Explanation

The closure of $A$ is $A, B, C, E, F$ and then $E \to DG$ adds $D, G$, which is everything, so $A$ is a key. $BC \to A$ makes $BC$ a key too. Every attribute is determined by $A$ or by $BC$ and neither is a subset of the other, so these are the only candidate keys (B is true, A is false). $E$ has the closure $\{E, D, G\}$, which is not all of R, so $E$ is not a key (C is false). The dependency $E \to DG$ has a left side that is not a superkey, which violates BCNF (D is true).