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)`A" "*" "B" "=" "(A" "-" "B) uu(B" "-" "A), AA""""A ," "B in P(X)` . Show that the empty set `varphi` is the identity for the

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

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 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=(A-B)uu(B-A) for all A,B in P(X) .Show that varphi is the identity element for * on P(X) .

If A and B are non empty sets,then (A-B)uu(B-A) equals

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

If A is an empty set and B is a set of vowels, then A nn B is a) A b) B c) A uu B d) none of these

If P(A) = P(B) = x and P(A cap B) = P(A'cap B')," then : " x=