GATE | GATE-CS-2017 (Set 2) | Question 24

Let L1 and L2 be any context-free language and R be any regular language. Then, which of the following is correct ?

I. L1 ∪ L2 is context-free.
II. L1' is context-free.
III. L1-R is context-free.
IV. L1 ∩ L2 context-free.

(A) I, II and IV only
(B) I and III only
(C) II and IV only
(D) I only

Answer: (B)

Explanation: Context free language are closed under union and difference with regular language.
It is not closed under complementation and intersection . Complement of CFL is recursive language .

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