1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
  3. Binary Operations
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Ex 1.4, 8 - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 16, 2024 by Teachoo

Transcript

Ex 1.4, 8 Let * be the binary operation on N defined by a * b = H.C.F. of a and b. Is * commutative? Is *associative? Does there exist identity for this binary operation on N? Check commutative * is commutative if a * b = b * a Since a * b = b * a ∀ a, b ∈ N * is commutative Check associative * is associative if (a * b) * c = a * (b * c) Since (a * b) * c = a * (b * c) ∀ a, b ∈ N * is associative Identity Element e is the identity of * if a * e = e * a = a i.e. HCF of a & e = HCF of e & a = a There is no value of e which satisfies the given condition Example: Let e = 1 HCF of a & 1 = 1 ≠ a HCF of 1 & a = 1 ≠ a Thus, there is no identity of * in N.

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

    3. Binary Operations

    Relations - Definition →
Relations - Definition →
Chapter 1 Class 12 Relation and Functions
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo