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QUESTION 3 (3.1) Define an operation on Z as follows: For a, b e Z+, 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?

QUESTION 3 (3.1) Define an operation on Z as follows: For a, b e Z+, 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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please with 3.1 and 3.2 and 3.3
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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