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We call the sharing of two languages L1 , L2 to be the set of all strings that are in both or neither of L1 and L2 . If L1 and L2 are regular, then the sharing of L1 and L2 is regular. True or false?

Apparently the answer is false but that confuses me because can't the sharing of L1 and L2 be all the strings that are neither in L1 and L2, which means that they could be nonregular strings? Or am I just not understanding this...

confused
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    You might want to edit your question to make it a question. – quicksort Jan 28 '17 at 23:53
  • http://cs.stackexchange.com/q/21897/755, http://cs.stackexchange.com/q/52853/755, http://cs.stackexchange.com/q/2851/755, http://cs.stackexchange.com/q/22000/755, https://en.wikipedia.org/wiki/Regular_language#Closure_properties – D.W. Jan 29 '17 at 00:56
  • Actually the complement of the symmetric difference of two regular languages is regular. This easily follows from classical closure properties. – Yuval Filmus Jan 29 '17 at 08:20

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