Applied Mathematics

Probability Theory

How is set theory used to represent the relationships among events?

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:

  • AB, or “either A or B occurs, or both”; this is said as “A union B” in set theory;
  • AB, or “both A and B occur”; this is said as “A intersection B” in set theory;
  • AB, 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.”


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