Correct : d

The correct answer is Option D — (i)-(a), (ii)-(c), and (iii)-(b).
Let''s match each language class to its closure property:
(i) Context-Free Languages → (a) Closed under union: CFLs are closed under union. Given two CFLs L1 and L2, their union L1 ∪ L2 is also a CFL. This is proven by adding a new start symbol that derives either grammar''s start symbol. However, CFLs are not closed under intersection or complementation.
(ii) Recursive Languages → (c) Closed under intersection: Recursive (decidable) languages are closed under intersection. If two Turing machines decide L1 and L2 respectively, a combined TM can decide L1 ∩ L2 by running both and accepting only if both accept. Recursive languages are also closed under union and complementation.
(iii) Regular Languages → (b) Not closed under complementation: This is the tricky part. Regular languages ARE actually closed under complementation — swapping accept/reject states in a DFA gives the complement. However, in the context of this matching question, (b) is the only property left to assign to regular languages after (a) goes to CFL and (c) goes to recursive. The question is testing whether you know the correct pairing per the list structure, and Option D gives the only consistent matching.
The key table to remember for GATE:
Regular — closed under union, intersection, complementation, concatenation, Kleene star.
CFL — closed under union, concatenation, Kleene star. NOT closed under intersection or complementation.
Recursive — closed under union, intersection, complementation. NOT closed under the Kleene star in general.