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Assume $L_1$ and $L_2$ two regular languages, and $L_1\subseteq L\subseteq L_2$. Does this imply that $L$ is a regular language?

Thanks in advance.

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Let $L_1=\emptyset$, $L_2=\Sigma^*$. I think not.

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    $\begingroup$ To add on a small bit, let $L = \{ 0^{n} 1^{n} : n \in \mathbb{N} \cup \{0\} \}$, the canonical non-regular, context-free grammar. We know that in this case, $L$ is not regular by the pumping lemma. $\endgroup$
    – ml0105
    Commented Apr 2, 2014 at 14:15

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