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Set of Non-Regular languages is Closed under Complementation Operation.

HOW??

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Take any non-regular language - its complement will be non regular because complement of complement of a language gives the same language and regular set is closed under complement. So, if we consider the set NON-REG for the set of all non-regular languages, it is closed under complement operation.
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CFL , recursive and CSL are all non regular language now let's say we take

CFL then it's complement will be recursive or CSL and

this both are non regular languages.

So we can say no regular languages are  closed under the complement.

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