[" Prose ther the relation B ca the set "2" of all integers defined by "(x,y)" a "R hArr x-y" is divisible by "n" is "],[" an equivalence relation on "Z" ."]

Let n be a positive integer.Prove that the relation R on the set Z of all integers numbers defined by (x,y)in R hArr x-y is divisible by n, is an equivalence relation on Z .

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

Let R be a relation on the set Z of all integers defined by:(x,y) in R implies(x-y) is divisible by n is eqivalence

Prove that the relation R on Z defined by (a,b)in R hArr a-b is divisible by 5 is an equivalence relation on Z .

Determine whether Relation R on the set Z of all integer defined as R={(x,y):y is divisible by x}

Let 'm' be a given positive integer. Prove that the relation, Congruence modulo m' on the set Z of all integers defined by : a equiv b(mod m) hArr (a-b) is divisible by m is an equivalence relation.

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.