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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
(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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- Spring '08
- The Land