GATE | GATE CS Mock 2018 | Set 2 | Question 24

Let L1, L2 be any two context-free languages and R be any regular language. Then which of the following is/are False?

(I) (L1)’∪L2∪L1 is context-free
(II) R’∪L2 is context-free
(III) R∩L1∩L2 is context-free
(IV) R∩L2 is 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 languages are not closed under complementary and intersection properties.
Therefore, statements (I), (III) are false.
Option (B) is correct.

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