12. Let E, F, and G be three events. Find expressions for the events so that of E, F, and G:
(a) only E occurs;
(b) both E and G but not F occur;
(c) at least one of the events occurs;
(d) at least two of the events occur;
(e) all three occur;
(f) none of the events occurs.
The solution gives expressions for the probability of the events.