GATE | GATE CS 1999 | Question 29

If L1 is a context free lenguage and L2 as a regular language, which of the following is/are False?

a.  L1-L2 is not context free

b.  L1 ∩ L2 is context free

c.  ~L1 is context free

d.  ~L2 is regular
(A) Only b
(B) Only c
(C) Both a and c
(D) Both b and c


Answer: (C)

Explanation: Given L1 is a context free language and L2 as a regular language then L1-L2 is context free language and ~L1(complement of context free) is not context free because context free is not closed under complement.

Complement of regular language i.e. ~L2 is also regular ( so d is correct ) since statements a and c are false.

Option (C) is correct.

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