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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

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    $\begingroup$ What have you tried? Hint: the emptyset is a regular language. $\endgroup$ – Bader Abu Radi Nov 10 at 14:24
  • $\begingroup$ I thought about $L$ \ $L^c$, but i'm not sure $\endgroup$ – Shay Doron Nov 11 at 8:37
  • $\begingroup$ 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. $\endgroup$ – Bader Abu Radi Nov 11 at 8:49
  • $\begingroup$ @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. $\endgroup$ – gnasher729 Nov 11 at 8:58
  • $\begingroup$ ok got it! $L$ \ $L$ = empty set! thx ! $\endgroup$ – Shay Doron Nov 11 at 11:02

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