a) Show that if A and B are sets, then A ? B = B ? A b) Show that if A and B are sets, then (A ? B) ? B = A. where ? is symmetric difference Solution A> LHS=A ? B=A U B - AB=(A+B-AB)-AB=A+B-2AB .......1 (where AB is the intersection of AB) NOW, RHS=B ? A=B U A +AB=(B+A-AB)-AB=A+B-2AB=LHS(proved) b> LHS=(A?B)?B=(A+B-2AB)?B (Put the expression of A?B) =A+B-2AB+B-2(A+B-2AB)B .....(IN EQN 1 PUT A= A+B-2AB) =A+2B-2AB-2AB-2B+4AB=A (PROVED).