GATE CSE 2020 Q46: What must hold for a relation in 3NF but not in BCNF

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

Try it: multiple choice: exactly one correct option

Wrong answer costs 2/3 mark in GATE.

Show answer and explanation

Answer: A (official GATE 2020 final answer key)

Concept used: BCNF needs every nontrivial FD to have a superkey on the left; 3NF also allows a prime attribute on the right.

First step: Not BCNF means some nontrivial $X \to A$ has $X$ not a superkey; being 3NF then forces $A$ to be prime.

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

Source: official GATE 2020 CS question paper and final answer key, organised by IIT Delhi. Question paper · Answer key