Pr oof:Left=(4∪B)-(4∩B)=(AUB)∩(A∩B) =(A∪B∩(A∪B)( De morgan'slms) =(∪B)∩A)∪(AUB)∩B)( distributi ve laws) =(A∩A)U(B∩A)∪(A∩B)∪(B∩B)( distributi ve laws) =(U(B-A)∪(A-B)∞)( complement laws) (A-B)U(B-A(identical laws, commutativ e lawsPr oof : Left = (A B) − (A B) = (A B)(A B) = (A B)(A  B) (De Morgan's laws) = ((A B) A)((A B) B) (distributi ve laws) = ((A A)(B A))(A B)(B B) (distributi ve laws) = ( (B − A))((A− B)) (complement laws) = (A− B)(B − A) (identical laws,commutativ e laws)