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Problem 1.1 Let A, B, C be three events in a sample space S. Each of the statements belovw describes an event built from events A, B, and C. For each statement, express the resulting event in terms of the events A, B, and C using only the complement, union, and intersection operations. Also, for cach statement, draw an appropriate Venn diagram and shade the resulting event. (There may be several ways to write the same statement, you only need to provide one.) (a) The outcome is in event A, but not in events B or C. (b) The outcome is in at most one of the events A or B, but not in both, and could be in neither. (c) The outcome is not in any of the events A, B or C (d) The outcome is both in event A and in event B, but not in event C. (e) The outcome is either in event A or, if it is not, then it is also not in event B.

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