Show that the relation R 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:

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

(P₁, P₂) ∈ R as the same polygon has the same number of sides.

∴ R is reflexive.

(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.

(P₁, P₂),(P₂, P₃) ∈ R

⇒ P₁ and P₂ have the same number of sides.

P₂ and P₃ have the same number of sides.

⇒ P₁ and P₃ have the same number of sides.

⇒ (P₁, P₃) ∈ 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