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GATE CS 2021 Official Paper: Shift 1

Option 4 : L_{1} - L_{2}

__Concepts:__

Operation under which context-free language is not closed: Intersection, complementation, set difference

Operation under which context-free language is closed: Union, Kleene Closure, and Concatenation.

Context-free language is closed under Intersection with regular language.

__Explanation:__

L1 is a regular and L2 is a context-free language.

Every regular language is context-free language.

__ Option 1:__ context-free language

\({L_1}.{L_2}\) it is the context-free language because it is closed under Concatenation.

__Option 2:__context-free language

L1 ∪ L2 it is the context-free language because it is closed under Union.

__Option 3:__ context-free language

\({L_1} \cap \;{L_2}\) it is the context-free language because context-free language is closed under Intersection with regular language.

__Option 4:__ may not be context-free language

L1 - L2 it may not be context-free language because it is not closed under complementation.

ST 1: General Awareness

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