Given a non-empty set X, consider the binary operation `*: P(X)xx P(X) ->P(X)`given by `A * B = AnnB AAA , B in P(X)`is the power set of X. Show that X is the identity element for this operation and X is the only invertible element i

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) .

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

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 S be a non-empty set and P(s) be the power set of set S.Find the identity element for all union () as a binary operation on P(S).

Write the power set p(x) of the set X={3,4}

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

Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b( mod 6). Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of a.

If the binary operation * on the set Z of integers is defined by a*b=a+b-5 then write the identity element for the operation * in Z .

Let P{X) denote the power set of X and A = {1,2}, then P(P(A)) contains m elements where m is equal to