TOC - Doubt closed

Question

As we know that the regular languages are closed under complement. That means if L is regular than it's complement will also be regular.

What about the non regular languages? Are they closed under complement? Can we say that if L is non regular than it's complement will also be not regular?

Please explain.

Answer 1

yes,

non-regular language complement should be non-regular...

why?

let say L=non-regular ===> L' is complement of non-regular

Assume L' is regular ===> (L')' is regular (due to regular languages are closed under complementation)

we know that (L')' = L ===> L is regular ===> contradiction

Therefore our assumption is wrong

L' should be non-regular

Comments

Thanks got it.