question_answer 69)

Given a non-emply set X, let * : P(X) × P(X)  be defined as A * B = (A ? B)  Show that the empty set  is the identity for the operation * and all the elements A of P(X) are invertible with A?1 = A. (Hint :  and (A ? A)

Answer:

Given * : P (X) × P (X)  defined as       A * B = (A ? B)         Ist Part : Let an identity element.                      Here                         = A       Also              is an identity element. 2nd part : Let                               So,        Every element of P(X) is invertible and A?1=A.