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If a language L is Context Free Language then what can we say about $L^-$ (Complement of L):

1. It is surely not Context Free Language?

2.It may or may not be Context Free Language?

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Closure property only tells us about the class of language when it holds for that class of language..If the property does not hold , it may or may not belong to that class..

Hence complement of a CFL may or may not be CFL..
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Hirak asked May 22, 2019
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is union of regular language and context free language always regular?