# Show that the relation R in the set A of all polygons as R = {(P_{1}, P_{2}) : P_{1} and P_{2} 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:**

R = {(P_{1}, P_{2}) : P_{1} and P_{2} have same number of sides}

(P_{1}, P_{2}) ∈ R as the same polygon has the same number of sides.

∴ R is reflexive.

(P_{1}, P_{2}) ∈ R

⇒ P1 and P2 have the same number of sides.

⇒ P_{2} and P_{1} have the same number of sides.

⇒ (P_{2}, P_{1}) ∈ R

∴ R is symmetric.

(P_{1}, P_{2}),(P_{2}, P_{3}) ∈ R

⇒ P_{1} and P_{2} have the same number of sides.

P_{2} and P_{3} have the same number of sides.

⇒ P_{1} and P_{3} have the same number of sides.

⇒ (P_{1}, P_{3}) ∈ R

∴ R is transitive.

R is an equivalence relation.

The elements in A related to the right-angled triangle (T) with sides 3, 4, 5 are those polygons that have three sides.

Set of all elements in a related to triangle T is the set of all right-angled triangles

NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.1 Question 13

## Show that the relation R in the set A of all polygons as R = {(P_{1}, P_{2}) : P_{1} and P_{2} 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?

**Summary:**

Hence, relation R in the set A of all polygons as R = {(P_{1}, P_{2}) : P_{1} and P_{2} have the same number of sides}, is an equivalence relation as it shows all the three properties i.e reflexive, symmetric, and transitive