Ex 1.1, 13 - Chapter 1 Class 12 Relation and Functions
Last updated at August 7, 2026 by Teachoo
To prove relation reflexive, transitive, symmetric and equivalent
What is reflexive, symmetric, transitive relation?
You are here
You are here
Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
-
To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
- To prove one-one & onto (injective, surjective, bijective)
- Composite functions
- Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 3 questions, selected from your answers, mistakes, and progress.
Transcript
Ex 1.1, 13 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? R = {(P1, P2): P1 and P2 have same the number of sides} Check reflexive P1 & P1 are the same polygon So, P1 & P1 have the same number of sides ∴ (P1 , P1) ∈ R So, R is reflexive. Check symmetric If P1 & P2 have the same number of sides, then P2 & P1 have the same number of sides, So, if (P1, P2) ∈ R , then (P2, P1) ∈ R ∴ R is symmetric. Check transitive If P1 & P2 have the same number of sides, and P2 & P3 have the same number of sides, then P1 & P3 have the same number of sides, So, if (P1, P2) ∈ R & (P2, P3) ∈ R, then (P1, P3) ∈ R ∴ R is transitive. Since, R is reflexive, symmetric and transitive. Hence, R 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? R = {(P1, P2): P1 and P2 have same the number of sides} Here, P1 = T, So, (T, P2) are in relation R So, T & P2 have same number of sides. So, P2 has 3 sides. So, P2 is set of all triangles Hence, the set of all elements in A related to triangle T is the set of all triangles.
