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Date: 16-1-2022
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An equivalence relation on a set is a subset of , i.e., a collection of ordered pairs of elements of , satisfying certain properties. Write "" to mean is an element of , and we say " is related to ," then the properties are
1. Reflexive: for all ,
2. Symmetric: implies for all
3. Transitive: and imply for all ,
where these three properties are completely independent. Other notations are often used to indicate a relation, e.g., or .
REFERENCES:
Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 18, 1990.
Stewart, I. and Tall, D. The Foundations of Mathematics. Oxford, England: Oxford University Press, 1977.
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