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(a) Consider (3,6) and (2,4) as elements of Z7xZ7. Compute (3,6) - (2,4). (b) Consider (3,6) and (2,4) as elements of R* x Z10. Compute (3,6)-(2,4).

(a) Consider (3,6) and (2,4) as elements of Z7xZ7. Compute (3,6) - (2,4). (b) Consider (3,6) and (2,4) as elements of R* x Z10. Compute (3,6)-(2,4).

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 do Exercise 15.2.13 part ABC and please show step by step and explain

Definition 15.2.12. Given two groups G and H, we define the product of groups G and H (denoted by GxH) as the set of pairs {(g, h), g = G, h = H}. If (gi, hi) and (g2, h2) are two elements of G x H, then we define the group operation (gi, h₁) o (92, h₂) as follows: (91, h₁) (92, h₂) : (9192, h₂h₂), where gig2 uses the group operation in G and hih2 uses the group operation in H. Exercise 15.2.13. (a) Consider (3,6) and (2, 4) as elements of ZxZ7. Compute (3,6) (2, 4). (b) Consider (3,6) and (2, 4) as elements of R*x Z10. Compute (3,6)-(2,4). 506 CHAPTER 15 INTRODUCTION TO GROUPS (c) Consider (3,6) and (2,4) as elements of Q*x Q. Compute (3,6)-(2,4).
Transcribed Image Text:Definition 15.2.12. Given two groups G and H, we define the product of groups G and H (denoted by GxH) as the set of pairs {(g, h), g = G, h = H}. If (gi, hi) and (g2, h2) are two elements of G x H, then we define the group operation (gi, h₁) o (92, h₂) as follows: (91, h₁) (92, h₂) : (9192, h₂h₂), where gig2 uses the group operation in G and hih2 uses the group operation in H. Exercise 15.2.13. (a) Consider (3,6) and (2, 4) as elements of ZxZ7. Compute (3,6) (2, 4). (b) Consider (3,6) and (2, 4) as elements of R*x Z10. Compute (3,6)-(2,4). 506 CHAPTER 15 INTRODUCTION TO GROUPS (c) Consider (3,6) and (2,4) as elements of Q*x Q. Compute (3,6)-(2,4).
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