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.
(a) Only E occurs: E \ F' \ G'
(b) Both E and G, but not F, occur: E \ F' \ G
(c) At least one of the events occurs: E ∪ F ∪ G
(a) To express the event that only E occurs, we can use the expression (E and not F and not G). This means that E happens, but both F and G do not happen.
(b) To express the event that both E and G occur, but not F, we can use the expression (E and G and not F). This means that both E and G happen, but F does not happen.
(c) To express the event that at least one of the events occurs, we can use the expression (E or F or G). This means that either E occurs, or F occurs, or G occurs, or any combination of these events occur.