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On the set of Z of integers define a relation by writing m [itex]\triangleright[/itex] n for m, n [itex]\in[/itex] Z.

m[itex]\triangleright[/itex]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/[itex]\triangleright[/itex] = {[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.

m[itex]\triangleright[/itex]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/[itex]\triangleright[/itex] = {[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.

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