For any events A and B in the same sample space , we define the symmetric difference of A and B to be the event

For any events A and B in the same sample space Ω, we define the symmetric difference of A and B to be the event (see next figure)

(i) Express in words what this event represents;
(ii) Show that the following hold:
AΔB = BΔA, AΔB = (A ∪ B) − AB, (AΔB)ΔB = A.

= AAB (AB)U (B-A). A B 02