# 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?

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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. –  DanielY Dec 7 '12 at 12:59
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? –  DanielY Dec 7 '12 at 13:15
If you take $L_1=L_2$ not regular, then $L=L_1$ satisfies your assumptions, but cannot be regular.