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(3.2) Define on Z by a*b = z, where z is the largest integer less than ab. (3.2.1) Show that is a binary operation on Z. * (3.2.2) What is 3* 5? (3.2.3) Is* commutative? (3.2.4) Is (2*3)*4 = 2 * (3 * 4)? Can you conclude that is associative?

(3.2) Define on Z by a*b = z, where z is the largest integer less than ab. (3.2.1) Show that is a binary operation on Z. * (3.2.2) What is 3* 5? (3.2.3) Is* commutative? (3.2.4) Is (2*3)*4 = 2 * (3 * 4)? Can you conclude that is associative?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.1: Finite Permutation Groups
Problem 1TFE: True or False Label each of the following statements as either true or false. 1. Every permutation...
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Please with 3.2
QUESTION 3 (3.1) Define an operation * on Z+ as follows: For a, beZ+, a*b = a - b + 1. Is a binary operation on Z+? Explain. (3.2) Define on Z by a * b = z, where z is the largest integer less than ab. (3.2.1) Show that is a binary operation on Z. (3.2.2) What is 3* 5? (3.2.3) Is commutative? (3.2.4) Is (2*3)*4 = 2 * (3 * 4)? Can you conclude that is associative?
Transcribed Image Text:QUESTION 3 (3.1) Define an operation * on Z+ as follows: For a, beZ+, a*b = a - b + 1. Is a binary operation on Z+? Explain. (3.2) Define on Z by a * b = z, where z is the largest integer less than ab. (3.2.1) Show that is a binary operation on Z. (3.2.2) What is 3* 5? (3.2.3) Is commutative? (3.2.4) Is (2*3)*4 = 2 * (3 * 4)? Can you conclude that is associative?
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