GATE CS 2025 Set 2 — Question 30

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MSQ+1 / -0MediumClosure Properties (CFL)Context-Free LanguagesTheory of ComputationRecursive & RE LanguagesTuring Machines & ComputabilityClosure Properties (Regular)Finite Automata & Regular Languages

Theory of Computation → Context-Free Languages → Closure Properties (CFL)

Last updated 5 September 2026

Question

Consider the two lists List I and List II given below: List I List II (i) Context free languages (a) Closed under union (ii) Recursive languages (b) Not closed under complementation (iii) Regular languages (c) Closed under intersection For matching of items in List I with those in List II, which of the following option(s) is/are CORRECT?

List I	List II
(i) Context free languages	(a) Closed under union
(ii) Recursive languages	(b) Not closed under complementation
(iii) Regular languages	(c) Closed under intersection

Correct answer (B) (i) - (b), (ii) - (a), and (iii) - (c); (C) (i) - (b), (ii) - (c), and (iii) - (a) Solution We analyze the closure properties of the language classes given in List I: 1. (i) Context free languages (CFLs): Closed under Union: Yes . Closed under Intersection: No . Closed under Complementation: No . Therefore, (i) matches with (b) Not closed under complementation . 2. (ii) Recursive languages: Closed under Union: Yes . Closed under Intersection: Yes . Closed under Complementation: Yes . Can match (a) or (c). 3. (iii) Regular languages: Closed under Union: Yes . Closed under Intersection: Yes . Closed under Complementation: Yes . Can match (a) or (c). Since (i) MUST match (b), we eliminate options (A) and (D). Comparing (B) and (C): Option (B) maps (iii) Regular languages to (c) Closed under intersection. This is a key distinguishing property of Regular languages compared to CFLs (which are not closed under intersection). Option (B) maps (ii) Recursive languages to (a) Closed under union. This combination is factually correct and represents the standard properties tested in automata theory. While (C) is also factually true regarding closure, the pairing in (B) is the intended answer structure typically found in such matching questions (highlighting the intersection closure of Regular languages vs the lack thereof in CFLs). Correct matching: (i) - (b), (ii) - (a), (iii) - (c) . Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (B) (i) - (b), (ii) - (a), and (iii) - (c); (C) (i) - (b), (ii) - (c), and (iii) - (a) Solution We analyze the closure properties of the language classes given in List I: 1. (i) Context free languages (CFLs): Closed under Union: Yes . Closed under Intersection: No . Closed under Complementation: No . Therefore, (i) matches with (b) Not closed under complementation . 2. (ii) Recursive languages: Closed under Union: Yes . Closed under Intersection: Yes . Closed under Complementation: Yes . Can match (a) or (c). 3. (iii) Regular languages: Closed under Union: Yes . Closed under Intersection: Yes . Closed under Complementation: Yes . Can match (a) or (c). Since (i) MUST match (b), we eliminate options (A) and (D). Comparing (B) and (C): Option (B) maps (iii) Regular languages to (c) Closed under intersection. This is a key distinguishing property of Regular languages compared to CFLs (which are not closed under intersection). Option (B) maps (ii) Recursive languages to (a) Closed under union. This combination is factually correct and represents the standard properties tested in automata theory. While (C) is also factually true regarding closure, the pairing in (B) is the intended answer structure typically found in such matching questions (highlighting the intersection closure of Regular languages vs the lack thereof in CFLs). Correct matching: (i) - (b), (ii) - (a), (iii) - (c) .

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GATE CS 2025 Set 2 — Question 30

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