Problem 5: (express the language in terms of basic set operations) a) Prove that if L1...

 

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Problem 5: (express the language in terms of basic set operations) a) Prove that if L1 and L2 are regular then L₁\L2 (set difference) is also regular. b) The symmetric difference of two sets S1 and S2 is defined as: SOS₂ = {x:xe S₁ or xe S₂ but x is not in both S1 and S2}. Show that the family of regular languages is closed under symmetric difference. Problem 5: (express the language in terms of basic set operations) a) Prove that if L1 and L2 are regular then L₁\L2 (set difference) is also regular. b) The symmetric difference of two sets S1 and S2 is defined as: SOS₂ = {x:xe S₁ or xe S₂ but x is not in both S1 and S2}. Show that the family of regular languages is closed under symmetric difference.