Let R(A, B, C, D, E) be a relational schema with functional dependency set F = \A BC,\ CD E,\ E A\. Which of the following statements is correct?

AD, ED and CD are the only candidate keys of R.

AD and ED are the only candidate keys of R.

A, E and CD are the only candidate keys of R.

A and CD are the only candidate keys of R.

GATE DA 2026 Q17: Candidate keys from functional dependencies

Let $R(A, B, C, D, E)$ be a relational schema with functional dependency set $F = \{A \to BC,\ CD \to E,\ E \to A\}$ .

Which of the following statements is correct?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

Show answer and explanation

Answer: A (official GATE 2026 final answer key)

Concept used: A candidate key is a minimal attribute set whose closure is all attributes.

First step: D appears on no right-hand side, so every key contains D; check $(AD)^+$ , $(ED)^+$ and $(CD)^+$ .

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key