   Chapter 8.3, Problem 6ES Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584

Solutions

Chapter
Section Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584
Textbook Problem

Determine whether the set forms a group with respect to the given operation. (You may assume the operation is associative.) If the set does not form a group, determine which properties fail.The even integers: multiplication

To determine

Determine whether the below set forms a group with respect to the given operation.

“The even integers; multiplication”

Explanation

Given: The set of even integers

Formula Used:

The given set forms group if the below three conditions are satisfied

1. The set should be closed with respect to the operation
2. The associative property of the operation should hold true for the elements of set
3. The identity element should exists in the operation for all the elements of set
4. For each element in the set has an inverse.

Calculation:

The set is given as

“All even integers”

Condition 1:

Let us suppose two even integers as 4 and 4

Now, find 4×(4)

Since 4×(4)=16 , which is an even integer

Thus, set of all even integers is closed with respect to the operation − multiplication

Condition 2:

Let us consider three even integers as 2 , 4 an

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