Partial order and equivalence relations
Posted on 2011-09-28
Hi guys: Can any one please tell me with example the difference between both of them Thanks.
A relation R on a set S is an equivalence relations if it satisfied all three of the following properties.
1. Reflexivity. For any a belongs S, a R a.
2. Symmetry. For any a, b belongs to S, a R b <--> b R a.
3. Transitivity. For any a,b, c belongs to S, if a R b and b R c, then a R c.
In other words. an equivalence relation is a relation that is reflexive, symmentric, and transitive.