Check sibling questions

Binary Operations

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

Ex 1.4, 8 - Chapter 1 Class 12 Relation and Functions

Last updated at May 29, 2023 by

Ex 1.4, 8 - Let a * b = HCF of a and b. Is * commutative - Whether binary commutative/associative or not

Ex 1.4, 8 - Chapter 1 Class 12 Relation and Functions - Part 2
Ex 1.4, 8 - Chapter 1 Class 12 Relation and Functions - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

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.

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.