Let A and B be events. The symmetric di?erence A?B is de?ned to be the set of all elements that are in A or B but not both. In logic and engineering, this event is also called the XOR (exclusive or)...

Let A and B be events. The symmetric di?erence A?B is de?ned to be the set of all elements that are in A or B but not both. In logic and engineering, this event is also called the XOR (exclusive or) of A and B. Show that P(A?B) = P(A) + P(B)-2P(AnB), directly using the axioms of probability.