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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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.
  • Priyanshu Kashyap's image
    Priyanshu Kashyap
    June 6, 2018, 3:26 p.m.
    Mana a is equal to question 1 2 3 Hai tab Siddiqui Je ke Aise sambandhu ki sankhya 3 Hai Jisme bracket a comma do aur bracket do, teen hai aur Jo sakoon Hai katha sangram ki to submit Nahi Hai Sidhe kijiye
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