Show that the relation R defined in the setAof all polygons as R = {(P1,P2):P1andP2have same number of sides}, is an equivalence relation. What is the set of all elements inArelated to the right angle triangleTwith sides 3, 4 and 5?

R = {(P1, P2): P1 and P2 have same the number of sides} R is reflexive since (P1, P1) ∈ R as the same polygon has the same number of sides with itself. Let (P1, P2) ∈ R. ⇒ P1 and P2­ have the same number of sides. ⇒ P2 and P1 have the same number of sides. ⇒ (P2, P1) ∈ R ∴R is symmetric. Now, Let (P1, P2), (P2, P3) ∈ R. ⇒ P1 and P2 have the same number of sides. Also, P2 and P3 have the same number of sides. ⇒ P1 and P3 have the same number of sides. ⇒ (P1, P3) ∈ R ∴R is transitive. Hence, R is an equivalence relation. The elements in A related to the right-angled triangle (T) with sides 3, 4, and 5 are those polygons which have 3 sides (since T is a polygon with 3 sides). Hence, the set of all elements in A related to triangle T is the set of all triangles. read less