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 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 ?

The relation R difined the set Z as R = {(x,y) : x - yin Z} show that R is an equivalence relation.

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

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

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 each of the relation R in the set A = { x in Z : 0 le x le 12} given by R = {(a,b):|a-b| is multiple of 4} is in equivelance.

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is

Show that the relation R in the set A of points in a plane give 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 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.

Let T be the set of all triangles in a plane with R a relation in T given by R ={(T _(1) , T _(2)): T _(1) is congruent to T _(2) } Show that R is an equivalence relation.