Ex 1.1, 4 - Show R = {(a, b) : a <= b} is reflexive, transitive - Ex 1.1

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  1. Chapter 1 Class 12 Relation and Functions
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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

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