# Quotient set of an equivalence relation

On the set of Z of integers define a relation by writing m $\triangleright$ n for m, n $\in$ Z.

m$\triangleright$n if m-n is divisble by k, where k is a fixed integer.

Show that the quotient set under this equivalence relation is:

Z/$\triangleright$ = {[0], [1], ... [k-1]}

I'm a bit new the subject of Set Theory so I'm a bit unsure as to how to go about solving this.

Last edited:

mathman
On the set of Z of integers define a relation by writing m $\triangleright$ n for m, n $\in$ Z.

If m-n is divisble by k, where k is a fixed integer then show that the quotient set under this equivalence relation is:

Z/$\triangleright$ = {[0], [1], ... [k-1]}

I'm a bit new the subject of Set Theory so I'm a bit unsure as to how to go about solving this.
$\triangleright$ seems to be undefined. You say it is a relationship without saying what it is.

sorry it wasn't clear from my post, i've rewritten the post to be a bit more clear.

The relationship is:
m$\triangleright$n, if m-n is divisble by k, where k is a fixed integer.

HallsofIvy