Given a non-empty set X, let * : P (X) → P (X) be defined as A * B = (A - B) ∪ (B - A) , ⟉ A, B ∈ P(X) . Show that the empty set Φ is the identity of the operation * and all the elements A of P(x) are invertible with A-1 = A.
(Hint : (A - Φ) ∪ ( Φ - A) = A and ( A - A) ∪ (A - A) = A * A = Φ).
