C- Compliment

I- Intersection

D- Difference (due to Intersection)

S- Subset

Q- Quotient

Subset and Inverse Homomorphism are not closed for any type of language

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**Answer is Option B**

__Option A __

CFL’s are **closed **under **CONCATENATION **operation & hence $L_1.L_2$ is necessarily a context free language.

__Option B__

CFL’s are **NOT closed **under **INTERSECTION **operation & hence $L_1 \cap L_2$ is **NOT NECESSARILY** a context free language.

__Option C__

CFL’s are **closed **under **INTERSECTION **operation with Regular language & hence $L_1 \cap R$ is necessarily a context free language.

__Option D__

CFL’s are **closed **under **UNION **operation & hence $L_1 \cup L_2$ is** **necessarily a context free language.

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