Let Z Z be the set of all integers and l...

Let `Z Z` be the set of all integers and let m be an arbitrary but fixed positive integer. Show that the relation "congruence modulo m" on `Z Z` defined by :
a `-=`b '(mod m)' `implies` (a-b) is divisible by m, for all a,b `in Z Z` is an equivalence relation on `Z Z`.

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Let `Z Z` be the set of all integers and let m be an arbitrary but fixed positive integer. Show that the relation "congruence modulo m" on `Z Z` defined by :
a `-=`b '(mod m)' `implies` (a-b) is divisible by m, for all a,b `in Z Z` is an equivalence relation on `Z Z`.