[" 13.Let "R" be a relation on the set "Z" of integers given by "(x,y)in R hArr|x-y|<=],[" Show that "R" is symmetric but not transitive."]

R is a relation on the set Z of integers and it is given by (x ,\ y) in RhArr|x-y|lt=1. Then, R is (a) reflexive and transitive (b) reflexive and symmetric (c) symmetric and transitive (d) an equivalence relation

R is a relation on the set Z of integers and it is given by (x ,\ y) in RhArr|x-y|lt=1. Then, R is (a) reflexive and transitive (b) reflexive and symmetric (c) symmetric and transitive (d) an equivalence relation

R relation on the set Z of integers and it is given by (x,y)in R hArr|x-y|<=1 then ,R is

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

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.Prove that (b) (x,y) in R implies(y,x) in R for all x,y,z in 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 .

R is a relation over the set of integers and it is given by (x,y) in R iff |x-y| le 1 . Then R is :

Let R be the relation on the set Z of all integers defined by R={(x, y) : x,y in Z,x-y is divisible by n}.Prove that i) (x, x) in R for all x in , Z ii) (x, y) in R implies that (y, x) in R for all x, y in Z iii) (x, y) in R and (y, z) in R implies that (x, z) in R for all x, y, z in Z

Let R be the relation on the Z of all integers defined by (x ,y) in R x-y is divisible by n . Prove that: (x ,x) in R for all x in Z (x ,y) in R (y ,x) in R for all x ,y in Z (x ,y) in Ra n d(y , z) in R (x ,z) in R for all x ,y ,z in R

If R is a relation defined on the set Z of integers by the rule (x,y)in R hArr x^(2)+y^(2)=9, then write domain of R.