Question 1191720
<font face="Times New Roman" size="+2">


An equivalence relation is a relation that is Reflexive, Symmetric, and Transitive:


Reflexive: *[tex \Large \forall (a,a)\ \in\ R\ on\ S, a\ -\ a\ =\ 0] therefore *[tex \Large R] is reflexive.


Symmetric: *[tex \Large \forall (a,b)\ \in\ R\ on\ S, a\ -\ b\ =\ 0\ \right\ b\ -\ a\ =\ 0] therefore *[tex \Large R] is symmetric.


Transitive: *[tex \Large \forall (a,b)\ &\ (b,c)\ \in\ R\ on\ S, \(a\ -\ b\ =\ 0\ \right\ a\ =\ b\ &\ b\ -\ c\ \right\ b\ =\ c)\ \right\ a\ =\ c\ \right\ a\ -\ c\ =\ 0] therefore *[tex \Large R] is transitive.


R is reflexive, symmetric, and transitive, therefore R is an equivalence relation.

																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
*[illustration darwinfish.jpg]

From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> 
I > Ø
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
{{n}\choose{r}}
</font>