GATE CS 2018 Set 1 — Question 17

MCQ+1 / -0.33MediumRecursive & RE LanguagesTuring Machines & ComputabilityTheory of Computation

Theory of Computation → Turing Machines & Computability → Recursive & RE Languages

Last updated 5 September 2026

Question

The set of all recursively enumerable languages is

Correct answer (B) closed under intersection. Solution Recursively Enumerable (RE) languages are closed under union, intersection, concatenation, and Kleene star. They are NOT closed under complementation (Recursive languages are). RE languages are a superset of Recursive languages. The set of all RE languages is countable because each is generated by a Turing Machine, and the set of TMs is countable. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (B) closed under intersection. Solution Recursively Enumerable (RE) languages are closed under union, intersection, concatenation, and Kleene star. They are NOT closed under complementation (Recursive languages are). RE languages are a superset of Recursive languages. The set of all RE languages is countable because each is generated by a Turing Machine, and the set of TMs is countable.

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