Ex 1.1, 10 (i) - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
To prove relation reflexive, transitive, symmetric and equivalent
What is reflexive, symmetric, transitive relation?
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Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
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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
Transcript
Ex 1.1, 10 Given an example of a relation. Which is (i) Symmetric but neither reflexive nor transitive. Let A = {1, 2, 3}. Let relation R on set A be Let R = {(1, 2), (2, 1)} Check Reflexive If the relation is reflexive, then (a, a) ∈ R for every a ∈ {1,2,3} Since (1, 1), (2, 2), (3, 3) ∉ R ∴ R is not reflexive Check Symmetric Since (1, 2) ∈ R , (2, 1) ∈ R So, If (a, b) ∈ R, then (b, a) ∈ R ∴ R is symmetric. Check transitive To check whether transitive or not, If (a, b) ∈ R & (b, c) ∈ R , then (a, c) ∈ R If a = 1, b = 2, but there is no c (no third element) Similarly, if a = 2, b = 1, but there is no c (no third element) Hence ,R is not transitive Hence, relation R is symmetric but not reflexive and transitive
