Abstract Algebra Notes

MAT3702 Assignment 1 (COMPLETE ANSWERS) 2026 - DUE 13 May 2026; 100% TRUSTED Complete, trusted solutions and explanations. For assistance, Whats-App 0.6.7-1.7.1-1.7.3.9. Ensure your success with us... 1. Let A,B,C be sets and show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). 2. Let G be a finite group with x, y ∈ G and prove that xy and yx have the same order. 3. Let G be a group such that every nonidentity element in G has order 2 and prove that G is abelian. 4. Show that ( ZZ, +) is a...

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14 pages

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Grade A+

EduPal

MAT3702 Assignment 1 (DETAILED ANSWERS) 2026 - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED Answers, guidelines, workings and references.. 1. Let A,B,C be sets and show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). 2. Let G be a finite group with x, y ∈ G and prove that xy and yx have the same order. 3. Let G be a group such that every nonidentity element in G has order 2 and prove that G is abelian. 4. Show that ( ZZ, +) is a subgroup of (Q| , +). 5. Show t...

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12 pages

Written in 2025/2026

Grade A+

VarsityC

Comprehensively structured MAT3702 Assignment 1 (ANSWERS) 2026 - DISTINCTION GUARANTEED. Prepared to a distinction standard with detailed and well-developed responses... 1. Let A,B,C be sets and show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). 2. Let G be a finite group with x, y ∈ G and prove that xy and yx have the same order. 3. Let G be a group such that every nonidentity element in G has order 2 and prove that G is abelian. 4. Show that ( ZZ, +) is a subgroup of (Q| , +). 5. Show...

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12 pages

Written in 2025/2026

Grade A+

Edge

MAT3702 Assignment 2 (COMPLETE ANSWERS) 2026 - DUE 19 August 2026; 100% TRUSTED Complete, trusted solutions and explanations. For assistance, Whats-App 0.8.1..2.7.8..3.3.7.2... Ensure your success with us...... 1. Prove that b | a if and only if (−b) | a. 2. If a | b and b | c, then prove that a | c. 3. Let R,S be rings and consider the following subsets of R × S R = {(r , 0S) | r ∈ R} and S = {(0R, s) | s ∈ S} where 0R ∈ R, 0S ∈ S are the zero elements in R,S respectively. (i...

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12 pages

Written in 2025/2026

Grade A+

EduPal

This document provides detailed workings, clear explanations, and well-structured solutions for the MAT3702 Assignment 2 (QUALITY ANSWERS) 2026 - For assistance call or Whats-App us on 0.8.1..2.7.8..3.3.7.2 .. 1. Prove that b | a if and only if (−b) | a. 2. If a | b and b | c, then prove that a | c. 3. Let R,S be rings and consider the following subsets of R × S R = {(r , 0S) | r ∈ R} and S = {(0R, s) | s ∈ S} where 0R ∈ R, 0S ∈ S are the zero elements in R,S respectively. (i) I...

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13 pages

Written in 2025/2026

Grade A+

StudyShack

MAT3702 Assignment 2 (DETAILED ANSWERS) 2026 - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED Answers, guidelines, workings and references.. 1. Prove that b | a if and only if (−b) | a. 2. If a | b and b | c, then prove that a | c. 3. Let R,S be rings and consider the following subsets of R × S R = {(r , 0S) | r ∈ R} and S = {(0R, s) | s ∈ S} where 0R ∈ R, 0S ∈ S are the zero elements in R,S respectively. (i) If R = ZZ3,S = ZZ5, then find R,S. (ii) Fo...

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11 pages

Written in 2025/2026

Grade A+

VarsityC

Comprehensively structured MAT3702 Assignment 2 (ANSWERS) 2026 - DISTINCTION GUARANTEED. Prepared to a distinction standard with detailed and well-developed responses... 1. Prove that b | a if and only if (−b) | a. 2. If a | b and b | c, then prove that a | c. 3. Let R,S be rings and consider the following subsets of R × S R = {(r , 0S) | r ∈ R} and S = {(0R, s) | s ∈ S} where 0R ∈ R, 0S ∈ S are the zero elements in R,S respectively. (i) If R = ZZ3,S = ZZ5, then find R,S. (ii)...

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10 pages

Written in 2025/2026

Grade A+

Edge

MAT3702 Assignment 1 (COMPLETE ANSWERS) 2026 - DUE 13 May 2026 1. Let A,B,C be sets and show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). 2. Let G be a finite group with x, y ∈ G and prove that xy and yx have the same order. 3. Let G be a group such that every nonidentity element in G has order 2 and prove that G is abelian. 4. Show that ( ZZ, +) is a subgroup of (Q| , +). 5. Show that A3 is a cyclic group of order 3. 6. Let G be an abelian group with a ∈ G and N a subgroup of G. ...

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12 pages

Written in 2025/2026

Grade A+

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8 pages

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masingaliyana