May 2024
Intermediate to advanced
332 pages
15h 45m
English
Content preview from Discrete Mathematics
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134 DISCRETE
MATHEMATIC..._---------------------------
3.3
EQUIVALENCE
RELATION
AND
PARTITIONS
Now we consider an important special type
of
relation, called an equivalence relation.
3.3.1
Definitions
Definition An equivalence relation is a relation that is reflexive, symmetric, and transitive. For example, the
"roommates" relation is
an
equivalence relation. So is "married to", "same size as", and "on same Ethernet
hub". A trivial example
is"="
relation on natural numbers. The hallmark
of
equivalence relation is the word
"same".
It
provides a way to "hide" unimportant differences.
Equivalence relations partition the universe into subsets in ...
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