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Question

Let L1L2 be any two context-free languages and R be any regular language. Then which of the following is/are CORRECT?
I. L1 L2 is context-free.
II. ¯L1 is context-free.
III. L1R is context-free.
IV. L1 L2 is context-free.

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Solution

I. L1 L2 is context-free = CFL CFL = CFL So, True
II. ¯L1 is context-free = ¯¯¯¯¯¯¯¯¯¯¯¯CFL=CSL but not CFL. So, False
III. L1R is context-free = CFL ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯Regular = CFL. So, True
IV. L1 L2 is context-free = CFL CFL = CSL. So,False

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