GATE | GATE CS 1996 | Question 33

If L1 and L2 are context free languages and R a regular set, one of the languages below is not necessarily a context free language, which one?
(A) L1 . L2
(B) L1 ∩ L2
(C) L1 ∩ R
(D) L1 ∪ L2

Answer: (B)

Explanation: Context free language are closed under union, concatenation and kleene closure but not closed under intersection and complement.
Therefore option (B) is not necessarily closed a context free language because it is not closed under intersection and context free intersection regular language is definitely context free language.

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