Show that the relation R in the set A of all the book 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 in the set A of all polygons as R={(P_1,P_2): P_1 and P_2 have the same number of sides },is an equivalence relation.What is the set of all elements in A related to the right angled triangle T with sides 3,4 and 5?

Show that the relation R. in the set A of all points in a place given by R = {(P,Q): the distance of the points P from 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 each of the relation R in the set A={x in Z: 0 le xle12} ,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 in each case.

Show that the relation 'S' in set A={x inz:0lexle12} given by S={(a,b):a.bin z,|a-b| is divisble by a} is an equivalence relation.

Show that the relation R in the set A = (1,2,3,4,5} given by R = {(a,b) : |a - b| is even }, is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1, 3, 5} is related to any element of {2,4}.

Show that the relation R in the set R of real number, defined as R = {(a.b): a lt= b^2} is neither reflexive nor symmetric nor transitive.

Show that the relation R on the set of natural numbers defined as R:{(x,y):y-x is a multiple of 2} is an equivalance relation

Show that each of the relation R in the set A={x in Z: 0lt= xlt=12} ,given by 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 in the set is given by A={x in Z,0lexle12} R={(a,b):a-b is a multiple of 4} is an equivalence relation.