# Abstract Algebra

• September 24th 2008, 06:25 PM
Juancd08
Abstract Algebra
Conversely if P is a partition of a set S, then there is some equivalence relation R on S such that P is the set of all equivalence classes.

I can prove the reverse but I need help going through it with this direction.
• September 24th 2008, 06:32 PM
ThePerfectHacker
Quote:

Originally Posted by Juancd08
Conversely if P is a partition of a set S, then there is some equivalence relation R on S such that P is the set of all equivalence classes.

I can prove the reverse but I need help going through it with this direction.

Define $E\subseteq S\times S$ so that $(a,b) \in E$ if and only if $a,b$ lie in the same partition set.