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[" 29.Let "R" be the set of real numbers...

[" 29.Let "R" be the set of real numbers."],[" Statement I "A={(x,y)in R times R:y-x" is a "],[~ integer}~ is~ an~ equivalence~ relation~ on~ R" ."]

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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 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 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 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.

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 .