Ex 1.4, 2 - Chapter 1 Class 12 Relation and Functions - Part 9

Advertisement

Ex 1.4, 2 - Chapter 1 Class 12 Relation and Functions - Part 10

Advertisement

Ex 1.4, 2 - Chapter 1 Class 12 Relation and Functions - Part 11

  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. (v) On Z+, define a * b = π‘Ž^𝑏 Check commutative * is commutative if a * b = b * a Since a * b β‰  b * a * is not commutative a * b = π‘Ž^𝑏 b * a = 𝑏^π‘Ž Check associative * is associative if (a * b) * c = a * (b * c) Example Let a = 2, b = 3, c = 4 (a * b)* c = (π‘Ž^𝑏) * c = (π‘Ž^𝑏 )^𝑐 a * (b * c) = a * (2^𝑏𝑐) = 2^(π‘Ž2^𝑏𝑐 ) (a * b)* c = (2 * 3) * 4 = (2^3) * 4 = 8 * 4 = 8^4 a * (b * c) = 2 * (3 * 4) = 2 * (3^4) = 2 * 81 = 2^81 Since (a * b) * c β‰  a * (b * c) * is not an associative binary operation

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
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.