- #1

dpa

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**Equivalence Principle: A hint on how to start!**

Hi, I have no idea where to start.

**1. Statement Problem**

Let X be a non empty set with a equivalence relation ~ on it. Prove that for all x,y[itex]\in[/itex]X,

[x]=[y] if and only if x~y.

## Homework Equations

For the Equivalence Relation to exist, it must be transitive, reflexive and symmetric.

## The Attempt at a Solution

I have no idea where to start. May be,

~ exists means that, x=y. But is self evident.

How do I prove the "only If" part as well?

Thank You.