Let R be the set of real numbers.
Statement 1:`A={(x,y) in R xx R : y-x` is an integer} is an equivalence relation on R.
Statement 2: `B= {x,y} in Rxx R : x=alpha y` for some rational number `alpha`} is an equivalence relation on R.

Let R be the set of real numbers Statement-1: A = {(x,y) in R xx R : y-x is an integer} is an equivalence relation on R. Statement -2 : B = {(x,y) in R xx R : x= alpha y for some relational number alpha } is an equivalence relation on R.

Let R be the set of real numbers. Statement-1 : A""=""{(x ,""y) in R""xx""R"":""y-x is an integer} is an equivalence relation on R. Statement-2 : B""=""{(x ,""y) in R""xx""R"":""x""=ay for some rational number a} is an equivalence relation on R.

Let R be the set of real numbers. Statement-1 : A""=""{(x ,""y) in R""xx""R"":""y-x is an integer} is an equivalence relation on R. Statement-2 : B""=""{(x ,""y) in R""xx""R"":""x""=alphay for some rational number a} is an equivalence relation on R. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. Statement-1 is true, Statement-2 is false. Statement-1 is false, Statement-2 is true.

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.

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

Let R be a relation in the set of natural numbers N defined by xRy if and only if x+y=18 . Is R an equivalence relation?

Show that the relation R on the set of natural numbers defined as R:{(x,y):y-x is a multiple of 2} is an equivalance relation