Assuming P ≠ NP, which of the following is TRUE?
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GATE CSE 2012 · Q4
Time
Select one answerSingle correct
Solution
Official answer: B) NP-complete ∩ P =
Turing Machines and UndecidabilityBy definition:
A language is in if and every problem in is polynomial-time reducible to .
If any problem could be solved in polynomial time (i.e., if ), then every problem in would be solvable in polynomial time, implying .
Therefore, under the assumption that , no problem can belong to . Hence:
This makes option (B) the correct statement.
Try the question first, then check your work.
Examiner trap
What would happen to the complexity class P = NP if even a single NP-complete problem belonged to P?
This Turing Machines and Undecidability previous year question is Q4 of the GATE CSE 2012 paper. Find more GATE CSE PYQs on Turing Machines and Undecidability in Theory of Computation, or browse all GATE CSE PYQs.
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Turing Machines and Undecidability has 30 GATE CSE PYQs across 20 papers from 2012 to 2026. 13 of them are 1-mark MCQs like this one, and GATE CSE 2012 has 2.
How GATE tests Turing Machines and UndecidabilityIndependent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.