GATE CSE 2021 Set 1 Q11: Closure of CFLs under operations with a regular language

Suppose that $L_1$ is a regular language and $L_2$ is a context-free language. Which one of the following languages is NOT necessarily context-free?

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Answer: C (official GATE 2021 final answer key)

Concept used: CFLs are closed under union, concatenation and intersection with a regular set, but not under complement.

First step: Write $L_1 - L_2 = L_1 \cap \overline{L_2}$ and take $L_1 = \Sigma^*$ .

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Source: official GATE 2021 Set 1 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key