If a relation `R` on the set `N` of natural numbers is defined as `(x,y)hArrx^(2)-4xy+3y^(2)=0,Aax,yepsilonN`. Then the relation `R` is

Let R be a relation on the set of natural numbers ,defined as R ={(x,y):x+2y=20, x,y varepsilon N} and x varepsilon {1,2,3,4,5} .Then ,the range of R is :

Given a relation R_(1) ,on the set R ,of real numbers,as R_(1)={(x,y):x^(2)-3xy+2y^(2)=0,x,y in R} .Is the relation R reflexive or symmetric?

The relation R on the set N of all natural numbers defined by (x,y)in R hArr x divides y, for all x,y in N is transitive.

Let R be a relation on the set of all real numbers defined by xRy hArr|x-y|<=(1)/(2) Then R is

Let R={(x,y):x^(2)+y^(2)=1,x,y in R} be a relation in R. Then the relation R is

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 .

Let 'R' be the relation defined on the of natural numbers 'N' as , R={(x,y):x+y=6} ,where x, y in N then range of the relation R is

Let N be the set of all natural numbers and we define a relation R={(x ,y):x, y in N , x+y is a multiple of 5} then the relation R is

Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as R = {(x, y) : 3x – y = 0} (ii) Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x lt 4} (iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x } (iv) Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x, y) : x and y work at the same place} (b) R = {(x, y) : x and y live in the same locality} (c) R = {(x, y) : x is exactly 7 cm taller than y } (d) R = {(x, y) : x is wife of y } (e) R = {(x, y) : x is father of y }