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

solution:

Case I:

R = {(P1, P2) :P1 and P2 have same number of sides}

Check for reflexive:

P1 and P1 have same number of sides, So R is reflexive.

Check for symmetric:

P1 and P2 have same number of sides then P2 and P1 have same number of sides, so (P1, P2)

∈ R and (P2, P1) ∈ R is symmetric.

Check for transitive:

Once more, P1 and P2 have same number of sides, and P2 and P3 have same number of sides, then, at that point additionally P1 and P3 have same number of sides .

So (P1, P2) ∈ R and (P2, P3) ∈ R and (P1, P3) ∈ R

R is transitive

In this manner, R is a comparable connection.

Since 3, 4, 5 are the sides of a triangle, the triangle is correct calculated triangle. In this manner, the set An is the arrangement of right calculated triangle.