This is the question I am asked and I am currently proving it using proof by contradiction something like this:
- Let's take some language L which is non regular.
- Let's assume compliment of L i.e. $(L^c)$ is regular.
Since we know that regular languages are closed under complementation, complementation of $(L^c)$, i.e. $(L^c)^c$ must be regular.
Now $(L^c)^c$ is $L$ means $L$ is regular which contradicts the assumption.
- So, our assumption that $L^c$ is regular must be false.
- Hence, we can prove that $L^c$ is not regular.
Is this a correct approach to deduce?
Using same result I have to state true/false for the following two statements and support by giving proof.
The class of non regular languages is closed under union.
The class of non regular languages is closed under intersection.
How do I solve these two statements using the result above? Any hints would be helpful.