Question 2

Question

What is an equivalence relation?

Answer

An equivalence relation $0\sim X$ is a relation on $\sim$ on $X$ such that:

1. $x\sim x$ (reflexive)
2. $x\sim y⟺y\sim x$ (symmetry)
3. $(x\sim y)\cap (y\sim z)⟹x\sim z$ (transitivity)
   For all $x,y,z\in X$.

Taken from Equivalence Relation