Let R be a relation on the set A of ordered pairs of positive integers defined by `(x , y) R (u , v)`if and only if `x v = y u`. Show that R is an equivalence relation.

Let R be a relation on the set A of ordered pairs of positive integers defined by (x,y)R(u,v) if and only if xv=yu Show that R is an equivalence relation.

Let R be a relation on the set A of ordered pairs of integers defined by (x,y)R(u,v) iff xv=yu .Show that R is an equivalence relation.

Let R be a relation on the set of all real numbers defined by xRy hArr|x-y|<=(1)/(2) Then R is

Let R be the relation in the set Z of all integers defined by R= {(x,y):x-y is an integer}. Then R is

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.

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.

Let n be a fixed positive integer. Define a relation R on Z as follows: (a , b)R a-b is divisible by ndot Show that R is an equivalence relation on Zdot

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 R be a relation on the set Q of all rationals defined by R={(a,b):a,binQ" and "a-binZ}. Show that R is an equivalence relation.