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Question 1. Let G = Q be the set of all rational numbers, and * = + be the usual addition operation on Q. Show that (Q, +) is a group. You need to show the following: 1. Closure: Q is closed under addition 2. Associativity: The addition operation is associative on Q 3. Identity: What is the identity element in (Q,+)? 4. Inverses: What is the additive inverse of each element in Q?

Question 1. Let G = Q be the set of all rational numbers, and * = + be the usual addition operation on Q. Show that (Q, +) is a group. You need to show the following: 1. Closure: Q is closed under addition 2. Associativity: The addition operation is associative on Q 3. Identity: What is the identity element in (Q,+)? 4. Inverses: What is the additive inverse of each element in Q?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question 1. Let G = Q be the set of all rational numbers, and * = + be the usual addition operation on Q. Show that (Q, +) is a group. You need to show the following: 1. Closure: Q is closed under addition 2. Associativity: The addition operation is associative on Q 3. Identity: What is the identity element in (Q, +)? 4. Inverses: What is the additive inverse of each element in Q?
Transcribed Image Text:Question 1. Let G = Q be the set of all rational numbers, and * = + be the usual addition operation on Q. Show that (Q, +) is a group. You need to show the following: 1. Closure: Q is closed under addition 2. Associativity: The addition operation is associative on Q 3. Identity: What is the identity element in (Q, +)? 4. Inverses: What is the additive inverse of each element in Q?
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