Ex 1.1, 4 - 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, 4 Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive and transitive but not symmetric. R = { (a, b) : a ≤ b } Here R is set of real numbers Hence, both a and b are real numbers Check reflexive We know that a = a ∴ a ≤ a ⇒ (a, a) ∈ R ∴ R is reflexive. Check symmetric To check whether symmetric or not, If (a, b) ∈ R, then (b, a) ∈ R i.e., if a ≤ b, then b ≤ a Since b ≤ a is not true for all values of a & b Hence, the given relation is not symmetric Check transitive If a ≤ b, & b ≤ c , then a ≤ c ∴ If (a, b) ∈ R & (b, c) ∈ R , then (a, c) ∈ R Hence, the given relation is transitive Hence, R = {(a, b) : a ≤ b}, is reflexive and transitive but not symmetric
