Let ∗ be the binary operation on N given by a ∗ b = L.C.M. of a and b. Find(i) 5 ∗ 7, 20 ∗ 16. (ii) Is ∗ commutative?(iii) Is ∗ associative? (iv) Find the identity of ∗ in N(v) Which elements of N are invertible for the operation ∗?

Let ∗ be the binary operation on N given by a ∗ b = L.C.M. of a and b. Find(i) 5 ∗ 7, 20 ∗ 16. (ii) Is ∗ commutative?(iii) Is ∗ associative? (iv) Find the identity of ∗ in N(v) Which elements of N are invertible for the operation ∗?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 43E: In Exercise , use generalized induction to prove the given statement. for all integers

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Question

Let ∗ be the binary operation on N given by a ∗ b = L.C.M. of a and b. Find
(i) 5 ∗ 7, 20 ∗ 16. (ii) Is ∗ commutative?
(iii) Is ∗ associative? (iv) Find the identity of ∗ in N
(v) Which elements of N are invertible for the operation ∗?

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