How is set theory used to represent the relationships among events?
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Statisticians often use the set theory to represent relationships among events (collections of outcomes of an experiment). This is usually written in the following notation, in which A and B are two events in the sample space S:
- A∪B, or “either A or B occurs, or both”; this is said as “A union B” in set theory;
- A∩B, or “both A and B occur”; this is said as “A intersection B” in set theory;
- A⊆B, or “if A occurs, so does B occur”; this is said as “A is a subset of B” in set theory;
- A’, or “A does not occur.”