A binary relation *R* on a set A is an *equivalence relation* if it is also a

There are multiple ways that equivalence relations are notated, but the most common are “*a* ~ *b*” and “*a* ≡ *b*” when it is obvious that a relation *R* is being referenced. Otherwise the equivalence may be denoted “*a* ~_{R}*b*“, “*a* ≡_{R}*b*“, or “*a*R*b*“.

So for every *a*, *b*, *c* in set A and

*a*~*a*(Reflexivity)- if
*a*~*b*if and only if*b*~ a (Symmetry) - if
*a*~*b*and*b*~*c*, then*a*~*c*(Transitivity)

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