menu
bartleby
search
close search
Hit Return to see all results
Subscribe
Sign in

Math
AlgebraElements Of Modern Algebra8th Edition

close solutoin list
Chapter 3.1, Problem 13E
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

Solutions

Chapter
Section
Problem 1TFE
Problem 2TFE
Problem 3TFE
Problem 4TFE
Problem 5TFE
Problem 6TFE
Problem 7TFE
Problem 8TFE
Problem 9TFE
Problem 10TFE
Problem 11TFE
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
1 views

In Exercises 1 − 14 , decide whether each of the given sets is a group with respect to the indicated operation. If it is not a group, state a condition in Definition 3.1 that fails to hold.

The set of all multiples of a positive integer n with operation addition.

To determine

Whether the set of all multiples of a positive integer n is a group with operation addition.

Explanation

Given information:

The set of all multiples of a positive integer n with operation addition.

Explanation:

Let us check if the set of all multiples of a positive integer n with operation addition is a group or not by using the definition given below:

Suppose the binary operation ∗ is defined for element of a set G. The set G is a group with respect to ∗, provided the following conditions hold.

1. G is closed under ∗. That is x∈G and y∈G imply that x∗y is in G.

2. ∗ is associative. For all x,y,z in G, x∗(y∗z)=(x∗y)∗z.

3. G has an identity element e. There is an e in G such that x∗e=e∗x=x for all x∈G.

4. G contains inverses. For each a∈G, there exists b∈G such that a∗b=b∗a=e.

Let n be any positive integer.

The set of all multiples of n is S={...,−3n,−2n,1n,0,1n,2n,3n,...}.

First condition:

Let x,y∈S such that x=pn,  y=qn   where p,  q∈ℤ  .

x+y=pn+qn=(p+q)n.

As p∈ℤ,q∈ℤ , p+q∈ℤ.

As x+y is also a multiple of n, x+y∈S

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution
arrow_back
Chapter 3.1,
Problem 12E
Chapter 3.1,
Problem 14E
arrow_forward

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 3 Solutions

Show all chapter solutions add
Sect-3.1 P-1TFESect-3.1 P-2TFESect-3.1 P-3TFESect-3.1 P-4TFESect-3.1 P-5TFESect-3.1 P-6TFESect-3.1 P-7TFESect-3.1 P-8TFESect-3.1 P-9TFESect-3.1 P-10TFE
Sect-3.1 P-11TFESect-3.1 P-1ESect-3.1 P-2ESect-3.1 P-3ESect-3.1 P-4ESect-3.1 P-5ESect-3.1 P-6ESect-3.1 P-7ESect-3.1 P-8ESect-3.1 P-9ESect-3.1 P-10ESect-3.1 P-11ESect-3.1 P-12ESect-3.1 P-13ESect-3.1 P-14ESect-3.1 P-15ESect-3.1 P-16ESect-3.1 P-17ESect-3.1 P-18ESect-3.1 P-19ESect-3.1 P-20ESect-3.1 P-21ESect-3.1 P-22ESect-3.1 P-23ESect-3.1 P-24ESect-3.1 P-25ESect-3.1 P-26ESect-3.1 P-27ESect-3.1 P-28ESect-3.1 P-29ESect-3.1 P-30ESect-3.1 P-31ESect-3.1 P-32ESect-3.1 P-33ESect-3.1 P-34ESect-3.1 P-35ESect-3.1 P-36ESect-3.1 P-37ESect-3.1 P-38ESect-3.1 P-39ESect-3.1 P-40ESect-3.1 P-41ESect-3.1 P-42ESect-3.1 P-43ESect-3.1 P-44ESect-3.1 P-45ESect-3.1 P-46ESect-3.1 P-47ESect-3.1 P-48ESect-3.1 P-49ESect-3.1 P-50ESect-3.1 P-51ESect-3.1 P-52ESect-3.2 P-1TFESect-3.2 P-2TFESect-3.2 P-3TFESect-3.2 P-4TFESect-3.2 P-5TFESect-3.2 P-6TFESect-3.2 P-1ESect-3.2 P-2ESect-3.2 P-3ESect-3.2 P-4ESect-3.2 P-5ESect-3.2 P-6ESect-3.2 P-7ESect-3.2 P-8ESect-3.2 P-9ESect-3.2 P-10ESect-3.2 P-11ESect-3.2 P-12ESect-3.2 P-13ESect-3.2 P-14ESect-3.2 P-15ESect-3.2 P-16ESect-3.2 P-17ESect-3.2 P-18ESect-3.2 P-19ESect-3.2 P-20ESect-3.2 P-21ESect-3.2 P-22ESect-3.2 P-23ESect-3.2 P-24ESect-3.2 P-25ESect-3.2 P-26ESect-3.2 P-27ESect-3.2 P-28ESect-3.2 P-29ESect-3.2 P-30ESect-3.2 P-31ESect-3.2 P-32ESect-3.3 P-1TFESect-3.3 P-2TFESect-3.3 P-3TFESect-3.3 P-4TFESect-3.3 P-5TFESect-3.3 P-6TFESect-3.3 P-7TFESect-3.3 P-8TFESect-3.3 P-9TFESect-3.3 P-10TFESect-3.3 P-11TFESect-3.3 P-1ESect-3.3 P-2ESect-3.3 P-3ESect-3.3 P-4ESect-3.3 P-5ESect-3.3 P-6ESect-3.3 P-7ESect-3.3 P-8ESect-3.3 P-9ESect-3.3 P-10ESect-3.3 P-11ESect-3.3 P-12ESect-3.3 P-13ESect-3.3 P-14ESect-3.3 P-15ESect-3.3 P-16ESect-3.3 P-17ESect-3.3 P-18ESect-3.3 P-19ESect-3.3 P-20ESect-3.3 P-21ESect-3.3 P-22ESect-3.3 P-23ESect-3.3 P-24ESect-3.3 P-25ESect-3.3 P-26ESect-3.3 P-27ESect-3.3 P-28ESect-3.3 P-29ESect-3.3 P-30ESect-3.3 P-31ESect-3.3 P-32ESect-3.3 P-33ESect-3.3 P-34ESect-3.3 P-35ESect-3.3 P-36ESect-3.3 P-37ESect-3.3 P-38ESect-3.3 P-39ESect-3.3 P-40ESect-3.3 P-41ESect-3.3 P-42ESect-3.3 P-43ESect-3.3 P-44ESect-3.3 P-45ESect-3.4 P-1TFESect-3.4 P-2TFESect-3.4 P-3TFESect-3.4 P-4TFESect-3.4 P-5TFESect-3.4 P-6TFESect-3.4 P-7TFESect-3.4 P-8TFESect-3.4 P-9TFESect-3.4 P-10TFESect-3.4 P-1ESect-3.4 P-2ESect-3.4 P-3ESect-3.4 P-4ESect-3.4 P-5ESect-3.4 P-6ESect-3.4 P-7ESect-3.4 P-8ESect-3.4 P-9ESect-3.4 P-10ESect-3.4 P-11ESect-3.4 P-12ESect-3.4 P-13ESect-3.4 P-14ESect-3.4 P-15ESect-3.4 P-16ESect-3.4 P-17ESect-3.4 P-18ESect-3.4 P-19ESect-3.4 P-20ESect-3.4 P-21ESect-3.4 P-22ESect-3.4 P-23ESect-3.4 P-24ESect-3.4 P-25ESect-3.4 P-26ESect-3.4 P-27ESect-3.4 P-28ESect-3.4 P-29ESect-3.4 P-30ESect-3.4 P-31ESect-3.4 P-32ESect-3.4 P-33ESect-3.4 P-34ESect-3.4 P-35ESect-3.4 P-36ESect-3.4 P-37ESect-3.4 P-38ESect-3.4 P-39ESect-3.4 P-40ESect-3.4 P-41ESect-3.4 P-42ESect-3.5 P-1TFESect-3.5 P-2TFESect-3.5 P-3TFESect-3.5 P-4TFESect-3.5 P-5TFESect-3.5 P-6TFESect-3.5 P-7TFESect-3.5 P-8TFESect-3.5 P-1ESect-3.5 P-2ESect-3.5 P-3ESect-3.5 P-4ESect-3.5 P-5ESect-3.5 P-6ESect-3.5 P-7ESect-3.5 P-8ESect-3.5 P-9ESect-3.5 P-10ESect-3.5 P-11ESect-3.5 P-12ESect-3.5 P-13ESect-3.5 P-14ESect-3.5 P-15ESect-3.5 P-16ESect-3.5 P-17ESect-3.5 P-18ESect-3.5 P-19ESect-3.5 P-20ESect-3.5 P-21ESect-3.5 P-22ESect-3.5 P-23ESect-3.5 P-24ESect-3.5 P-25ESect-3.5 P-26ESect-3.5 P-27ESect-3.5 P-28ESect-3.5 P-29ESect-3.5 P-30ESect-3.5 P-31ESect-3.5 P-32ESect-3.5 P-33ESect-3.5 P-34ESect-3.5 P-35ESect-3.5 P-36ESect-3.5 P-37ESect-3.5 P-38ESect-3.5 P-39ESect-3.6 P-1TFESect-3.6 P-2TFESect-3.6 P-3TFESect-3.6 P-4TFESect-3.6 P-5TFESect-3.6 P-6TFESect-3.6 P-7TFESect-3.6 P-8TFESect-3.6 P-9TFESect-3.6 P-10TFESect-3.6 P-1ESect-3.6 P-2ESect-3.6 P-3ESect-3.6 P-4ESect-3.6 P-5ESect-3.6 P-6ESect-3.6 P-7ESect-3.6 P-8ESect-3.6 P-9ESect-3.6 P-10ESect-3.6 P-11ESect-3.6 P-12ESect-3.6 P-13ESect-3.6 P-14ESect-3.6 P-15ESect-3.6 P-16ESect-3.6 P-17ESect-3.6 P-18ESect-3.6 P-19ESect-3.6 P-20ESect-3.6 P-21ESect-3.6 P-22ESect-3.6 P-23ESect-3.6 P-24ESect-3.6 P-25E

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Simplify the algebraic expressions in Problems 15-34 by removing parentheses and combining similar terms. Objec...

Intermediate Algebra

Sketching the Graph of an Equation In Exercises 19-28, sketch the graph of the equation. Use a graphing utility...

Calculus: An Applied Approach (MindTap Course List)

The Capital MGT fund has total assets of $25,000,000 and liabilities of $3,500,000. If there are 8,600,000 shar...

Contemporary Mathematics for Business & Consumers

In Exercises 4756, solve the given equation for the indicated variable. 1,000=500(1.12t) (Round the answer to f...

Finite Mathematics and Applied Calculus (MindTap Course List)

In Problems 23-30, round all calculations to 2 decimal places. 24. Present value Suppose that the rate of flow ...

Mathematical Applications for the Management, Life, and Social Sciences

Expand Your knowledge: Harmonic Mean When data consist of rates of change, such as speeds, the harmonic mean is...

Understanding Basic Statistics

A model for the yield Y of an agricultural crop as a function of the nitrogen level N and phosphorus level P in...

Calculus (MindTap Course List)

Matching In Exercises 5-10, match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e),...

Calculus: Early Transcendental Functions

What is a vector function? How do you find its derivative and its integral?

Multivariable Calculus

According to a July 31, 2013, posting on cnn.com subsequent to the death of a child who bit into a peanut, a 20...

Probability and Statistics for Engineering and the Sciences

Absolute Value Inequalities Solve the absolute value inequality. Express the answer using interval notation and...

Precalculus: Mathematics for Calculus (Standalone Book)

Note: Exercise preceded by an asterisk are of a more challenging nature. a In the figure, are lines m, n, and p...

Elementary Geometry For College Students, 7e

Solve the equations in Exercises 126. 14x2=0

Finite Mathematics

Solve the following problems. a. A repeated-measures study with a sample of n = 16 participants produces a mean...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Use Definition II to explain why it is possible to find an angle that will make tan as large as we wish.

Trigonometry (MindTap Course List)

Fibonacci Sums Make a conjecture for each of the following sums, where Fn represent the nth Fibonacci number. a...

Mathematical Excursions (MindTap Course List)

Solve the equations in Exercises 112 for x (mentally, if possible). 3x+1=x

Applied Calculus

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded? 72. an = c...

Calculus: Early Transcendentals

Given that limx2f(x)=4limx2g(x)=2limx2h(x)=0 find the limits that exist. If the limit does not exist, explain w...

Single Variable Calculus

The following scores are the ages for a random sample of n = 30 drivers who were issued speeding tickets in New...

Statistics for The Behavioral Sciences (MindTap Course List)

Give the number of significant digits (the accuracy) of each measurement: 20.00 m

Elementary Technical Mathematics

At St. Algebra College, the math department ran some special sections of the freshman math course using a varie...

Essentials Of Statistics

There exists a function f such that f(1) = 2, f(3) = 0, and f(x) 1 for all x.

Single Variable Calculus: Early Transcendentals, Volume I

POPULATION Growth A major corporation is building a 4325-acre complex of homes, offices, stores, schools, and c...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Using Parametric Equations In Exercises 5-22, sketch the curve represented by the parametric equations (indicat...

Calculus of a Single Variable

Finding Discontinuities Using Technology In Exercises 71-74, use a graphing utility to graph the function. Use ...

Calculus: Early Transcendental Functions (MindTap Course List)

ODDS OF MAKING A SALE Carmen, a computer sales person, believes that the odds are 8 to 5 that she will clinch t...

Finite Mathematics for the Managerial, Life, and Social Sciences

A formula for the derivative of a function f is given. How many critical numbers does f have? f(x) = 5e0.1|x| s...

Single Variable Calculus: Early Transcendentals

The figure at the right shows one point P on a conic and the distances of P to the focus and the directrix of a...

Study Guide for Stewart's Multivariable Calculus, 8th

Example 9.3 gave the following airborne times (in minutes) for 10 randomly selected flights from San Francisco ...

Introduction To Statistics And Data Analysis

An integral for the surface area obtained by rotating y = sin x + cos x, , about the x-axis is:

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

If the ratio of the measure of the complement of an angle to the measure of its supplement is 1:3, find the mea...

Elementary Geometry for College Students

Precalculus or Calculus In Exercises 3-6.decide whether the problem can be solved using precalculus or whether ...

Calculus

Fill in the blanks. fgx= __________

College Algebra (MindTap Course List)

Using the Table of Block Thicknesses for a Customary Gage Block Set, determine a combination of gage blocks for...

Mathematics For Machine Technology

Explain the circumstances in which an ABAB reversal design should be modified to create a more complex phase-ch...

Research Methods for the Behavioral Sciences (MindTap Course List)

Business Schools of Asia-Pacific The pursuit of a higher education degree in business is now international. A s...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Answer the following questions using complete sentences and your own words. HANDS ON Think of something that y...

Mathematics: A Practical Odyssey

Setting Up a Triple IntegralIn Exercises 13-18, set up a triple integral for the volume of the solid. Do not ev...

Calculus (MindTap Course List)

Under what circumstances would you use a multiple-baseline design instead of an ABAB (reversal) design?

Research Methods for the Behavioral Sciences (MindTap Course List)

For the week ended January 15, 2009, the bullish sentiment of individual investors was 27.6% (AAII Journal, Feb...

Statistics for Business & Economics, Revised (MindTap Course List)

Finding the Divergence of a Vector Field In Exercises 61-64, find the divergence of the vector field at the giv...

Multivariable Calculus

bartleby
© bartleby 2019