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[" A cluen a non-empty set "X" ,let "*" ? Justify your answe "],[[" 13.Given a non-empty set "X," let "*:P(X)times P(X)rarr P(X)" be "," be "," be "],[A^(*)B=(A-B)uu(B-A),AA A,B in P(X)" .Show that the empt "," empt "],[" identity for the peration "*" and all the elements "A" of "P(X)" are in "],[A^(-1)=A" .(Hint : "(A-phi)uu(phi-A)=A" and "(A-A)uu(A-A)=" in "],[" 14.Define a binary operation "*" on the seat "]]

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Given a non-empty set X, let **: P(X) xx P (X) to P (X) be defined as A **B = (A-B) uu (B-A) , AA A, B in P (X). Show that the empty set phi is the identity for the opertion ** and all the elements A of P (X) are invertible with A ^(-1) =A.

Given a non-empty set X, let **: P(X) xx P (X) to P (X) be defined as A **B = (A-B) uu (B-A) , AA A, B in P (X). Show that the empty set phi is the identity for the opertion ** and all the elements A of P (X) are invertible with A ^(-1) =A.

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Let X be a non-empty set and let * be a binary operation on P\ (X) (the power set of set X ) defined by A*B=(A-B)uu(B-A) for all A ,\ B in P(X)dot Show that varphi is the identity element for * on P\ (X) .

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