A Partition Defines an Equivalence Relation.
Let A={a,b,c,d,e} and let C={{a,b,c},{d,e}}.
Which relations are equivalence relations?
Equivalence relations are relations that have the following properties:
- They are reflexive: A is related to A.
- They are symmetric: if A is related to B, then B is related to A.
- They are transitive: if A is related to B and B is related to C then A is related to C.
Is equivalence a relation?
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The relation "is equal to" is the canonical example of an equivalence relation. Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes.
