3. Answer the following questions with proof. 3a) Show that if the pair of events (A, B) are independent, then so are the pairs (not A, B), (A, not B), and (not A, not B). 3b) Show that the sure event is independent of all other events. Also the impossible event is independent of all other events. 3c) Consider an infinite sample space, say the set of points (x, y) on the plane where 0