(c) From (a) and (b), we already show by definition that A is indeed an algebra. Can you explain why A is not a o-algebra? (Hint: consider the sets Ai = {2i -1} so that Al = {1}, A2 = {3}, etc.; is it true that U. A; E A?).In this exercise, let's look at an example of algebra that is not a o-algebra. Suppose sample space is the set of all positive numbers S' = {1, 2, 3, . . . }. Define the set of events A = {AC S : A is a finite set or A is a finite set}. (a) Prove that if A E A, then we have AC E A. (b) Prove that if A1, A2 E A, then we have A1 U A2 E A. (Hint: note that if A] is not a finite set, then (Al U A2) must be a finite set. Why?)