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

Let T be the set of all triangles in a plane with R a relation in T given by {(T_1,T_2):T_1~=T_2} show that R is an equivalence relation.

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: 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 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.

In the set of all natural numbers,let a relation defined by {(a,b):a,binN,a-b is divisible by 5} .Prove that R 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.

Let R = {(a,b): a le b ^(2)} be a relation on the set of all real numbers. Then R is

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.