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Date: 14-2-2017
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Date: 29-12-2021
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Date: 9-1-2022
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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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