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Consider Z₁1 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Part A. Denote by +11 the operation "addition modulo 11" where a +11 b is the remainder when a + b is divided by 11. 1. Construct the operation table for +₁₁ on the set Z₁1. 2. What is the identity element of Z₁₁ under +11? 3. Determine the inverse of each element of Z₁₁ with respect to +11.

Consider Z₁1 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Part A. Denote by +11 the operation "addition modulo 11" where a +11 b is the remainder when a + b is divided by 11. 1. Construct the operation table for +₁₁ on the set Z₁1. 2. What is the identity element of Z₁₁ under +11? 3. Determine the inverse of each element of Z₁₁ with respect to +11.

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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Consider Z₁1 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Part A. Denote by +11 the operation "addition modulo 11" where a +11 b is the remainder when a + b is divided by 11. 1. Construct the operation table for +11 on the set Z₁1. 2. What is the identity element of Z₁₁ under +11? 3. Determine the inverse of each element of Z₁₁ with respect to +11.
Transcribed Image Text:Consider Z₁1 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Part A. Denote by +11 the operation "addition modulo 11" where a +11 b is the remainder when a + b is divided by 11. 1. Construct the operation table for +11 on the set Z₁1. 2. What is the identity element of Z₁₁ under +11? 3. Determine the inverse of each element of Z₁₁ with respect to +11.
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