The relation ‘is parallel to’, on the set A of all coplanar straight lines is an equivalence relation.

Show that the relation ‘is perpendicular to' on the set A of all coplanar straight lines is symmetric but it is neither reflexive nor transitive.

Show that relation R = {(L_1, L_2) : L_1 is parallel to L_2 }, defined on the set of all lines, is an equivalence relation.

Show that relation R = {(T_1, T_2) : T_1 is similar to T_2 }, defined on the set of all triangles, is an equivalence relation.

Which one of the following relations on RR is an equivalence relation ?

Show that the relation ‘is a factor of’ on the set N of all natural numbers is reflexive and transitive but not symmetric.

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.

Let A be the set of all students of class XII in a school and R be the relation, having the same sex on A, and then prove that R is an equivalence relation.

Show that relation R = {(P_1, P_2) : P_1 and P_2 have same numbers of sides}, defined on the set of all polygons is an equivalence relation