Ex 1.4, 2 - Chapter 1 Class 12 Relation and Functions - Part 3

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Ex 1.4, 2 - Chapter 1 Class 12 Relation and Functions - Part 4

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  1. Chapter 1 Class 12 Relation and Functions (Term 1)
  2. Serial order wise

Transcript

Ex 1.4, 2 For each binary operation * defined below, determine whether * is commutative or associative. (ii) On Q, define a * b = ab + 1 Check commutative * is commutative if a * b = b * a Since a * b = b * a ∀ a, b ∈ Q * is commutative a * b = ab + 1 b * a = ba + 1 = ab + 1 Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c ≠ a * (b * c) * is not an associative binary operation (a * b)* c = (ab + 1) * c = (ab + 1)c + 1 = abc + c + 1 a * (b * c) = a * (bc + 1) = a(bc + 1) + 1 = abc + a + 1 a * (b * c) = a * (bc + 1) = a(bc + 1) + 1 = abc + a + 1

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.