For a sequence of events, {En, n > 1}, prove the following: (a) The union bound, P «ΣΡ (Ε.) i=1 (b) If En increasing), t

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For a sequence of events, {En, n > 1}, prove the following: (a) The union bound, P «ΣΡ (Ε.) i=1 (b) If En increasing), then lim P (En) = P (lim En) Also using the fact that Em ), argue that the same is true for decreasing sequences. Hint: In both parts construct another sequence, {Fn, n > 1), of mutually exclusive events for which U, F; = U- E;. n-> 1200