Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have same number of pages} is an equivalence relation.

Show that the relation R on the set A of all the books in a library of a college given by R={(x,y):x and y have the same number of pages }, is an equivalence relation.

Show that the relation R ,defined on the set A of all polygons as R={(P_(1),P_(2)):P_(1) and P_(2) have same number of sides } ,is an equivalence relation.What is the sides all elements in A related to the right angle triangle T with sides 3,4 and 5?

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 .

Show that the relation is congruent to on the set of all triangles in a plane is an equivalence relation

Show that the relation R in the set A={x: x in N,x <=10} given by R={(a, b):a+ b is even number] is an equivalence relation. Also find the set of all elements related to 3

Show that the relation R on the set Z of integers,given by R={(a,b):2 divides a-b}, is an equivalence relation.

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 }

Show that each of the relation R in the set A={x in Z:0<=x<=12} given by (i) R={(a,b):|a-b| is a multiple of 4} (ii) quad R={(a,b):a=b} is an equivalence relation.Find the set of all elements related to 1 in each case.

Show that the relation R on the set A of points in a plane, given by R={(P , Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further show that the set of all points related to a point P!=(0, 0) is the circle passing through P with origin as centre.

Show that the relation R on the set A={x in Z:0<=x<=12}, given by R={(a,b):|a-b| is a multiple of 4} is an equivalence relation.Find the set of all elements related to 1 i.e.equivalence class [1]