The GATE Grind

GATE 2025 CS (CS2) – Question 46

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

Consider the following relational schema along with all the functional dependencies that hold on them.

R1(A, B, C, D, E): { $D \to E,\ EA \to B,\ EB \to C$ }
R2(A, B, C, D): { $A \to D,\ A \to B,\ C \to A$ }

Which of the following statement(s) is/are TRUE?

  1. R1 is in 3NF
  2. R2 is in 3NF
  3. R1 is NOT in 3NF
  4. R2 is NOT in 3NF

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Show answer and explanation

Correct answer: (C) R1 is NOT in 3NF; (D) R2 is NOT in 3NF

Explanation

R1's only candidate key is AD (prime attributes A, D). $D \to E$ has a non-superkey LHS and a non-prime RHS, so R1 is not in 3NF. R2's only key is C, and $A \to D$ has a non-superkey LHS with non-prime D, so R2 is not in 3NF.