# set difference of two non regular languages

Lets say we have $$L_1$$ and $$L_2$$ two non regular languages . is $$L_1$$\ $$L_2$$ is always non-regular languages? I thought about $$L$$ \ $$L^c$$, but i'm not sure

• What have you tried? Hint: the emptyset is a regular language. – Bader Abu Radi Nov 10 at 14:24
• I thought about $L$ \ $L^c$, but i'm not sure – Shay Doron Nov 11 at 8:37
• If you want to refute the claim, the difference must be regular. $L \setminus L^C = L$, so i don't see how it helps. But you're close. – Bader Abu Radi Nov 11 at 8:49
• @Shay Why wouldn’t you be sure? L minus L complement equals L, therefore is not regular. You can be 100% sure about that. Think about how you can subtract something from L that destroys the non-regularity. – gnasher729 Nov 11 at 8:58
• ok got it! $L$ \ $L$ = empty set! thx ! – Shay Doron Nov 11 at 11:02