Let n be the number of sides of a polygon P1.
R = {(P1, P2): P1 and P2 are n sided polygons}.
(i) (a) Any polygon P1 has n sides ⇒ R is reflexive.
(b) If P1 has n sides, P2 also has n sides, then if P2 has n sides, P1 also has n sides.
⇒ R is symmetric.
(c) Let P1, P2; P2, P3 are pairs of n sided polygons. Thus, P1 and P3 are also n sided polygons.
⇒ R is transitive.
Hence, R is an equivalence relation.
(ii) The set A = set of all the triangles in a plane.