Consider the following relational schema along with all the functional dependencies that hold on them. R1(A, B, C, D, E): \D E,\ EA B,\ EB C\ R2(A, B, C, D): \A D,\ A B,\ C A\ Which of the following statement(s) is/are TRUE?

GATE CSE 2025 Session 2 Q46: Which of two relations with given FDs are in 3NF

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?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

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Answer: C, D (official GATE 2025 final answer key)

Concept used: 3NF: for every non-trivial FD $X \to Y$ , $X$ is a superkey or every attribute of $Y$ is prime.

First step: Find the candidate keys ( $AD$ for R1, $C$ for R2) and test $D \to E$ and $A \to D$ .

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Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key