question_answer 13)

Show that the relation R defined in the set A of all polygons are R = {P1, P2} : P1 and P2 have same number of sides} is an equivalence relation. What is the set of al elements in A related to the right angle triangle T with sides 3, 4 and 5 ? 

Answer:

Let A be the set of all polygons.       R = {(P1, P2) : P1 and P2 have same number of sides}              is reflexive.       Symmetric : Let (P1, P2)        and P2 have the same number ofsides        have the same number of sides              is symmetric.       Transititive : Let (P1, P2)  and (P2, P3)        and P2 have the same number of sides and P2 and P3 have the same number of sides.        and P3 have the same number of sides                        is transitive.       Hence R is an equivalence relation.       Let B be the set of all polygons related to the right angled triangle T with sides 3, 4 and 5. Therefore set B contains all polygons with three sides.        where P is a polygon of three sides}.