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Chapter 1 Class 12 Relation and Functions
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Ex 1.4, 2 - Chapter 1 Class 12 Relation and Functions - Part 5

Ex 1.4, 2 - Chapter 1 Class 12 Relation and Functions - Part 6

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Transcript

Ex 1.4, 2 For each binary operation * defined below, determine whether * is commutative or associative. (iii) On Q, define a * b = ab/2 Check commutative * is commutative if a * b = b * a Since a * b = b * a βˆ€ a, b ∈ Q * is commutative a * b = π‘Žπ‘/2 b * a = π‘π‘Ž/2 = π‘Žπ‘/2 Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) βˆ€ a, b, c ∈ Q * is an associative binary operation (a * b)* c = (π‘Žπ‘/2) * c = (π‘Žπ‘/2 Γ— 𝑐)/2 = π‘Žπ‘π‘/4 a * (b * c) = a * (𝑏𝑐/2) = (π‘Ž Γ— 𝑏𝑐/2)/2 = π‘Žπ‘π‘/4

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.