Subset of A Regular Language

Question

I need to show that a subset of a regular language is regular or not. I think it may not be regular but I could not find a counter example.

Do you have any simple example to prove that?

Thanks in advance.

Answer 1

Let $N$ be some non-regular language over some alphabet $\Sigma$. You should know several examples of non-regular languages.

Then $$N\subset \Sigma^\ast$$

and $\Sigma^\ast$ is regular.

Answer 2

Let $L_1 = \{ a^mb^n \}_{m,n,}$, $L_2 = \{ a^nb^n \}_n$. $L_2 \subset L_1$.

$L_1$ is regular, $L_2$ is not..