Ex 1.1, 1 (i) - Chapter 1 Class 12 Relation and Functions
Last updated at August 5, 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, 1 Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1, 2, 3…13, 14} defined as R = {(x, y): 3x − y = 0} R = {(x, y): 3x − y = 0} So, 3x – y = 0 3x = y y = 3x where x, y ∈ A ∴ R = {(1, 3), (2, 6), (3, 9), (4, 12)} Check Reflexive If the relation is reflexive, then (a, a) ∈ R for every a ∈ A i.e. {1, 2, 3…13, 14} Since (1, 1) ∉ R ,(2, 2) ∉ R , (3, 3) ∉ R , …. (14, 14) ∉ R ∴ R is not reflexive Check symmetric To check whether symmetric or not, If (a, b) ∈ R, then (b, a) ∈ R Here (1, 3) ∈ R , but (3, 1) ∉ R ∴ R is not symmetric Check transitive To check whether transitive or not, If (a,b) ∈ R & (b,c) ∈ R , then (a,c) ∈ R Here, (1, 3) ∈ R and (3, 9) ∈ R but (1, 9) ∉ R. ∴ R is not transitive Hence, R is neither reflexive, nor symmetric, nor transitive.
