Let `Z` be the set of all integers and `R` be the relation on `Z` defined as `R={(a , b); a ,\ b\ in Z ,` and `(a-b)` is divisible by `5.}` . Prove that `R` is an equivalence relation.

Let Z be the set of all integers and R be the relation on Z defined by R= { (a,b): a, b in Z and (a-b) is divisible by 5} . Prove that R is an equivalence relation

Let m be a given fixed positive integer. Let R={(a.b) : a,b in Z and (a-b) is divisible by m} . Show that R is an equivalence relation on Z .

Let Z be the set of all integers and Z_0 be the set of all non zero integers. Let a relation R on Z X Z_0 be defined as follows: (a , b)R(c , d) ,a d=b c for all (a , b),(c , d) ZXZ_0 Prove that R is an equivalence relation on ZXZ_0dot

Let N be the set of all natural numbers and let R be a relation on NxxN , defined by (a ,\ b)R\ (c ,\ d) a d=b c for all (a ,\ b),\ (c ,\ d) in NxxN . Show that R is an equivalence relation on NxxN

Let S be the set of all real numbers and Let R be a relations on s defined by A R B hArr |a|le b. then ,R is

Let Z be the set of all integers and Z_0 be the set of all non-zero integers. Let a relation R on ZxxZ_0 be defined as follows: (a , b)R(c , d) if and only if a d=b c for all (a , b),(c , d) in ZxxZ_0 Prove that R is an equivalence relation on ZxxZ_0 .

Let Z be the set of all integers and Z_0 be the set of all non-zero integers. Let a relation R on ZxxZ_0 be defined as follows: (a ,\ b)\ R\ (c ,\ d)hArra d=b c for all (a ,\ b),\ (c ,\ d) in ZxxZ_0 Prove that R is an equivalence relation on ZxxZ_0

Let N be the set of all natural numbers and let R be a relation on N×N , defined by (a , b)R(c , d) iff a d=b c for all (a , b),(c , d) in N × Ndot . Show that R is an equivalence relation on N × N .

Let R be the relation on Z defined by R={(a , b): a , b in Z , a-b is an integer }dot Find the domain and range of Rdot

Let R be the relation on Z defined by R = {(a , b): a , b in Z , a b is an integer}.Find the domain and range of R.