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

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

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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. (iii) On Q, define a * b = ab/2 Check commutative * is commutative if a * b = b * a Since a * b = b * a โˆ€ a, b โˆˆ Q * is commutative a * b = ๐‘Ž๐‘/2 b * a = ๐‘๐‘Ž/2 = ๐‘Ž๐‘/2 Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) โˆ€ a, b, c โˆˆ Q * is an associative binary operation (a * b)* c = (๐‘Ž๐‘/2) * c = (๐‘Ž๐‘/2 ร— ๐‘)/2 = ๐‘Ž๐‘๐‘/4 a * (b * c) = a * (๐‘๐‘/2) = (๐‘Ž ร— ๐‘๐‘/2)/2 = ๐‘Ž๐‘๐‘/4

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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.