A relation R is defined on the set of all natural numbers IN by: `(x,y)inRimplies(x-y)` is divisible by 5 for all `x,y inIN`. Prove that R is an equivalence relation on IN.

A relation R is defined on the set of all natural numbers NN by : (x,y) in Rimplies (x-y) is divisible by 6 for all x,y,in NN prove that R is an equivalence relation on NN .

A relation R on the set of natural number N N is defined as follows : (x,y) in R to (x-y) is divisible by 5 for all x,y in N N Prove that R is an equivalence relation on N N .

A relation R is defined on the set of all integers Z Z follows : (x,y) in "R" implies (x,y) is divisible by n Prove that R is an equivalence relation on Z Z .

A relation R is defined on the set of natural numbers NN as follows : (x,y)in R rArr y is divisible by x, for all x, y in NN . Show that, R is reflexive and transitive but not symmetric on NN .

A relation R is defined on the set NN of natural number follows : (x,y) in R implies x divides y for all x,y in NN show that R is reflexive and transitive but not symmetric on NN .

A relation R is defined on the set of natural numbers NN follows : (x,y) in R implies x+y =12 for all x,y in NN Prove that R is symmetric but neither reflexive nor transitive on NN .

A relation R is defined on the set N N of natural number follows : (x,y) in "R" implies x+2y=10, for all x,y in N N Show that R is antisymmetric on N N

The relation R defined on the set N N of natural numbers by xRy iff 2x^(2) -3xy +y^(2) =0 is

A relation R is defined on the set N N of natural as follows : (x,y) in "R" implies x-y+ sqrt(3) is an iR Rational number for all x,y in N N . Show that R is reflexive on N N .

A realation rho is defined on set Z , a set of all integers , such that rho ={(x,y) in Z xx Z :Y -x is divisible by 5} . Discuss whether rho is an equialence relation . IF A ={x in Z: (2 ,x) in rho , -10 le x le 10} then mention the elements of A .