One event is said to exclude another event if an

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Unformatted text preview: ments and intersections or unions. For example, if A is any event, then A ∪ Ac = Ω and AAc = ∅. The complement of Ω is ∅, and vice versa. A bit more terminology is introduced before we describe the axioms precisely. One event is said to exclude another event if an outcome being in the first event implies the outcome is not in the second event. For example, the event O excludes the event E. Of course, E excludes O as well. Two or more events E1 , E2 , . . . , En , are said to be mutually exclusive if at most one of the events can be true. Equivalently, the events E1 , E2 , . . . , En are mutually exclusive if Ei Ej = ∅ whenever i = j. That is, the events are disjoint sets. De Morgan’s law in the theory of sets is that the complement of the union of two sets is the intersection of the complements. Or vice versa: the complement of the intersection is the union of the complements: (A ∪ B )c = Ac B c (AB )c = Ac ∪ B c . (1.1) De Morgan’s law is easy to verify using the Karnaugh map for two events, shown in Figure 1.1. B c B cc AB c AB Bc c Bc B A AB AB A...
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