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 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 triangle as R={(T_1,T_2):T_1 is similar to T_2 ,is an equivalence relation. Consider three right angled triangles T_1 with sides 3,4,5, T_2 with sides 5,12,13 and T_3 with sides 6,8,10. Which triangle among T_1,T_2 and T_3 are related ?

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 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.

Let L be the set of all line in XY place and R be the relation in L defined as R = {(L_1,L_2):L_1 is parallel to L_2 }Show that R is an equivalence relation. Find the set of all line related to the line y=2x+4

The relation R defined in the set A={-1,0,1} as R={(a,b):a=b^2} Is R 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 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 numbers defined as R={(a,b):aleb^2} is neither reflexive, nor symmetric, nor transitive.