Let `f: X to Y` be a function. Define a relation R in X given by `R = {(a,b):f (a) =f (b)}.` Examine whether R is an equivalence relation or not.

Relation R on Z defined as R = {(x ,y): x - y "is an integer"} . Show that R is an equivalence relation.

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b) : |a-b| is even}, is an equivalence relation.

Show that the relation R in the set A= {1,2,3,4,5} given by R= "{"(a,b):|a-b| is even} is an equivalence relation.

Prove that the relation R in the set of integers Z defined by R = {(x,y) : x - y. is an integer) is an equivalence relation.

Prove that the relation R in the set of integers z defined by R = { ( x , y) : x-y is an integer } is an equivalence relation.

Let N denote the set of all natural numbers and R be the relation on NxN defined by (a , b)R(c , d), a d(b+c)=b c(a+d)dot Check whether R is an equivalence relation on NXNdot

Solve that the relation R in the set z of intergers given by R={(x,y):2 divides (x-y)} is an equivalence relation.

Let R be the equivalence relation on z defined by R = {(a,b):2 "divides" a - b} . Write the equivalence class [0].

Show that the relation R in the set of all integers, Z defined by R = {(a, b) : 2 "divides" a - b} is an equivalence relation.

Show that the relation R in the set A={x in Z :0lexle12} is given by R={(a,b) : |a-b|" is a multiple of 4"} is an equivalence relation .