# 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?

What about $L_1 = L_2$? – Hendrik Jan Dec 7 '12 at 12:57
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
If you take $L_1=L_2$ not regular, then $L=L_1$ satisfies your assumptions, but cannot be regular.