16 Is the set of numbers described belowa group under the given operation?Integers; additionYesNo

Answered: ers; addition Yes

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ers; addition Yes

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter1: Variables, Expressions, And Integers

Section1.3: Order Of Operations

Problem 1E

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Question

Is the set of numbers described belowa group under the given operation?
Integers; addition
Yes
No

Expert Solution

Step 1

the set of integers under addition must satisfy following properties to be a group

1. closure property

the addition of two integers is again a integer, therefore closure property is satisfied.

2. Associative property

let $a, b, c \in Z$ where Z is set of integers

Therefore $(a + b) + c = a + (b + c)$

the associative property also holds true,

3. Existence of identity

0 is the identity element

4. Existence of inverse.

for an element $a \in Z$ , the inverse is -a

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