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

Show that the relation R defined in 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 set of all elements in A related to the right angle triangle T with sides 3,4 and 5 ?

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

Show that the relation R, on the set A={x in ZZ : 0 le x le 12} given by R = {(a,b) : |a-b| is a multiple of 4 and a,b in A } is an equivalance relation on A.

Show that the relation R in 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 ne (0,0) is the circle passing through P with origin as centre.

A relation R is defined on the set of integers Z Z as follows R= {(x,y) :x,y inZ Z and (x-y) is even } show that R is an equivalence relation on Z Z .

Let R be a relation on the set A of ordered pairs of positive integers defined by (x,y) R (u,v) if and only if xv = yu. Show that R is an equivalence relation.

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

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 .