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

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 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 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 '*'

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)

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. '*'

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.