Solution Found!

Math / Contemporary Abstract Algebra 8 / Chapter 2 / Problem 7E

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

Change Question

Give two reasons why the set of odd integers under

Chapter 2, Problem 7E

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Give two reasons why the set of odd integers under addition is not a group.

Questions & Answers

QUESTION:

Give two reasons why the set of odd integers under addition is not a group.

ANSWER:

Step 1 of 2

For a set to be called a Group, the set should follow the rules of Property of Closure, Property of Associativity, Existence of identity and inverse.

According to the Property of Closure over Addition, the sum of two numbers from a set should belong to the set itself.

But in the case of a set of odd numbers, the result of addition is always an even number, which does belong to the set of odd numbers.

Study Tools You Might Need

Chapter: Problem: 11

Fundamentals of Physics 10
Figure 23-35 shows a closed Gaussian surface in the shape of a cube of edge length 2.00 m,with one corner at x1 5.00 m,y1 4.00 m.The cube lies in a region where the electric field vector is given by with y in meters.What is the net charge contained by the cube? E : $ '3.00i ' 4.00y2 j " 3.00k N/C Fig

Chapter: 1 Problem: 49P

Chemistry 11
Carry out the following conversions: (a) 1.42 light- years to miles (a light-year is an astronomical measure of distancethe distance traveled by light in a year, or 365 days; the speed of light is \(3.00 \times 10^{8}\) m/s). (b) 32.4 yd to centimeters, (c) \(3.0 \times 10^{10}\) cm/s to ft/s.

Chapter: Problem: 1

Myers' Psychology for AP 2
By seeking to measure atoms of the mind, who established the first psychology laboratory? a. Sigmund Freud b. John B. Watson c. Wilhelm Wundt

Chapter: 16 Problem: 16.2(b)

Physical Chemistry 8
Calculate (a) the thermal wavelength, (b) the translational partition function of an Ar atom in a cubic box of side 1.00 cm at (i) 300 K and (ii) 3000 K.

Chapter: 15 Problem: 8

Campbell Biology in Focus - Standalone book 1
Imagine you want to study one of the mouse crystallins, proteins present in the lens of the eye. Assuming the gene has been cloned, describe two ways you could investigate expression of this gene in the developing mouse embryo

Chapter: 3 Problem: 2

Human Biology 11
Jogging is considered aerobic exercise because the cardio-vascular system (heart and blood vessels) can adjust to supply the oxygen needs of working cells. In contrast, sprinting the 100-meter dash might be called anaerobic (lacking oxygen) exercise, and golf non aerobic exercise. Explain these last

Chapter: 14 Problem: 1

Life-Span Human Development 9
Laura Carstensens socioemotional selectivity theory suggests that adults narrow their social networks with age to better meet their emotional needs. Develop some alternative hypotheses about why elderly adults have smaller social networks than young adults.

Chapter: 6 Problem: 1

General Chemistry. Principles and Modern Applications 11
Convert each pressure to an equivalent pressure in atmospheres. (a) 736 mmHg; (b) 0.776 bar; (c) 892 Torr; (d) 225 kPa

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account