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- Assume that is a binary operation on a non empty set A, and suppose that is both commutative and associative. Use the definitions of the commutative and associative properties to show that [ (ab)c ]d=(dc)(ab) for all a,b,c and d in A.Assume that is an associative binary operation on the non empty set A. Prove that a[ b(cd) ]=[ a(bc) ]d for all a,b,c, and d in A.