Let X be a nonempty set and *be a binary operation on `P(X),` the power set of `X,` defined by `A * B=A nn B` for all `A, B in P(X).` (

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=AuuB for all A ,\ B in P(X) . Prove that * is both commutative and associative on P(X) . Find the identity element with respect to * on P(X) . Also, show that varphi in P(X) is the only invertible element of P(X)dot

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=AuuB for all A , B in P(X) . Prove that * is both commutative and associative on P(X) . Find the identity element with respect to * on P(X) . Also, show that varphi in P(X) is the only invertible element of P(X)dot

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) .Show that varphi is the identity element for * on P(X) .

Let A be a non-empty set and '*' be a binary operation on P(A), the power set of A, defind by X*Y = X uu Y for all X, Y in P(A) Show that phi in P (A) is only invertible element w.r.t '*'

Let A be a non-empty set and '*' be a binary operation on P(A), the power set of A, defind by X*Y = X uu Y for all X, Y in P(A) find the identity element w.r.t. '*'

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) .

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) .

A is a non empty set and let*be a binary operation an P(A)the prower set of A defined by X**Y=XcapY for X, YinP(A) (i) Show that A*B=B* A for A, BinP(A)

A is a non empty set and let*be a binary operation an P(A)the prower set of A defined by X**Y=XcapY for X, YinP(A) (ii)Show that * is associative.