# Proving or disproving regularity of a language

The question is as follows:

```` If L1 and L2 are not regular and L1 ⊆ L ⊆ L2, then L is regular
````

My intuition says that it's wrong so I've been looking for a counterexample, so far I didn't succeed.

Can I please get a direction? is this claim might be true?

Thanks in advance

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1
What about $L_1 = L_2$? – Hendrik Jan Dec 7 '12 at 12:57
I don't think I may do that. Besides, even if L1=L2, I can find a language L that is contained in it and regular, so it doesn't disproves the claim. – user1067083 Dec 7 '12 at 12:59

2
If $L_1=L_2$ is not regular, then $L=L_1$ saisfies all conditions, and cannot be regular. If that is not what you need or want, please rephrase the question. You might want to add "for all" or "there exist". – Hendrik Jan Dec 7 '12 at 13:02
No, that's probably the counterexample I was looking for, thanks alot :) Can you leave an answer so I can accept it? – user1067083 Dec 7 '12 at 13:15

## 1 Answer

If you take $L_1=L_2$ not regular, then $L=L_1$ satisfies your assumptions, but cannot be regular.

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