A relation R is defined on the set of integers `Z Z` as follows
R= {(x,y) :x,y `inZ Z` and (x-y) is even }
show that R is an equivalence relation on `Z Z`.

A relation R is defined on the set of integers Z as follows: R{(x,y):x,y in Z and x-y" is odd"} Then the relation R on Z is -

A relation R is defined on the set of all integers Z Z follows : (x,y) in "R" implies (x,y) is divisible by n Prove that R is an equivalence relation on Z Z .

A relation S is defined on the set of real numbers R R a follows: S={(x,y) : s,y in R R and and x= +-y} Show that S is an equivalence relation on R R .

A relation R on the set of integers Z is defined as follows : (x,y) in R rArr x in Z, |x| lt 4 and y=|x|

A realation rho is defined on set Z , a set of all integers , such that rho ={(x,y) in Z xx Z :Y -x is divisible by 5} . Discuss whether rho is an equialence relation . IF A ={x in Z: (2 ,x) in rho , -10 le x le 10} then mention the elements of A .

A relation R on the set of natural number N N is defined as follows : (x,y) in R to (x-y) is divisible by 5 for all x,y in N N Prove that R is an equivalence relation on N N .

Let Z be the set of all integers and R be the relation on Z defined as R={(a , b); a ,\ b\ in Z , and (a-b) is divisible by 5.} . Prove that R is an equivalence relation.

A relation R on the set of complex number is defined by z_1 R z_2 iff (z_1 - z_2)/(z_1+z_2) is real ,show that R is an equivalence relation.

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 .