# Are there regular languages between every two non-regular languages?

I have a question regarding regular languages. Given that $L_1$ and $L_2$ are non-regular languages, can a regular language $L$ exist so it is a subset of $L_2$ and $L_1$ subset of $L$?

To be more specific:

$\qquad L_1 \subset L \subset L_2$

for $L_1, L_2$ non-regular Languages.

• Do you mean $\subseteq$ or $\subsetneq$? Do we know $L_1 \subseteq L_2$? And: What have to tried, where did you get stuck? – Raphael Feb 12 '14 at 7:56

## 1 Answer

Hint. Given any sets $A, B, C$ we have $A \cap C \subset C \subset B \cup C$.

• Thx for you answer you really guided to the solution! – Mario Feb 11 '14 at 19:29
• Might be interesting to give languages $A \cap C, B \cup C, C$ that fulfill the desired properties. – G. Bach Feb 11 '14 at 20:32
• Please consider not to encourage undesired posting behaviour. – Raphael Feb 12 '14 at 8:29