Let R be a relation defined on the set Z of all integers and `x Ry` when `x + 2y` is divisible by 3. then

Let R be a relation defined on the set Z of all integers and xRy when x+2y is divisible by 3.then

Let RR be a relation defined on the set ZZ of all integers and xRy when x+2y is divisible by 3, then

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 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 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 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

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.

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 .