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 R is defined on the set of all natural numbers IN by: (x,y)inRimplies(x-y) is divisible by 5 for all x,y inIN . Prove that R is an equivalence relation on IN.

A relation R is defined on the set of all natural numbers NN by : (x,y) in Rimplies (x-y) is divisible by 6 for all x,y,in NN prove that R is an equivalence relation on NN .

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 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 .

A relation R is defined on the set N N of natural number follows : (x,y) in "R" implies x+2y=10, for all x,y in N N Show that R is antisymmetric on N N

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 is defined on the set of natural numbers NN follows : (x,y) in R implies x+y =12 for all x,y in NN Prove that R is symmetric but neither reflexive nor transitive on NN .

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 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 is defined on the set NN of natural number follows : (x,y) in R implies x divides y for all x,y in NN show that R is reflexive and transitive but not symmetric on NN .