BuyFind*arrow_forward*

8th Edition

Gilbert + 2 others

Publisher: Cengage Learning,

ISBN: 9781285463230

Chapter 1.4, Problem 11E

Textbook Problem

Prove or disprove that the set

**a.** addition defined on

**b.** multiplication defined on

Elements Of Modern Algebra

Show all chapter solutions

Ch. 1.1 - True or False Label each of the following...Ch. 1.1 - True or False
Label each of the following...Ch. 1.1 - True or False
Label each of the following...Ch. 1.1 - True or False Label each of the following...Ch. 1.1 - True or False Label each of the following...Ch. 1.1 - True or False Label each of the following...Ch. 1.1 - True or False
Label each of the following...Ch. 1.1 - True or False
Label each of the following...Ch. 1.1 - True or False Label each of the following...Ch. 1.1 - True or False Label each of the following...

Ch. 1.1 - For each set A, describe A by indicating a...Ch. 1.1 - 2. Decide whether or not each statement is true...Ch. 1.1 - Decide whether or not each statement is true. (a)...Ch. 1.1 - 4. Decide whether or not each of the following is...Ch. 1.1 - Evaluate each of the following sets, where U={...Ch. 1.1 - 6. Determine whether each of the following is...Ch. 1.1 - Write out the power set, (A), for each set A. a....Ch. 1.1 - 8. Describe two partitions of each of the...Ch. 1.1 - Write out all the different partitions of the...Ch. 1.1 - 10. Suppose the set has a .
a. How many elements...Ch. 1.1 - 11. State the most general conditions on the...Ch. 1.1 - 12. Let Z denote the set of all integers, and...Ch. 1.1 - 13. Let Z denote the set of all integers, and...Ch. 1.1 - In Exercises 1435, prove each statement. ABABCh. 1.1 - In Exercises 1435, prove each statement. (A)=ACh. 1.1 - In Exercises , prove each statement.
16. If and ,...Ch. 1.1 - In Exercises , prove each statement.
17. if and...Ch. 1.1 - In Exercises , prove each statement.
18.
Ch. 1.1 - In Exercises , prove each statement.
19.
Ch. 1.1 - In Exercises 1435, prove each statement. (AB)=ABCh. 1.1 - In Exercise 14-35, prove each statement.
21.
Ch. 1.1 - In Exercise 14-35, prove each statement. A(AB)=ABCh. 1.1 - In Exercises 14-35, prove each statement.
23.
Ch. 1.1 - In Exercise 14-35, prove each statement....Ch. 1.1 - In Exercise 14-35, prove each statement. If AB,...Ch. 1.1 - In Exercise 14-35, prove each statement.
26. If...Ch. 1.1 - In Exercise 14-35, prove each statement.
27.
Ch. 1.1 - In Exercise 14-35, prove each statement. A(BA)=Ch. 1.1 - In Exercises 14-35, prove each statement.
29.
Ch. 1.1 - In Exercises 14-35, prove each statement....Ch. 1.1 - In Exercises 1435, prove each statement....Ch. 1.1 - In Exercises 1435, prove each statement....Ch. 1.1 - In Exercises , prove each statement.
33.
Ch. 1.1 - In Exercises , prove each statement.
34. if and...Ch. 1.1 - In Exercises 1435, prove each statement. AB if and...Ch. 1.1 - Prove or disprove that AB=AC implies B=C.Ch. 1.1 - Prove or disprove that AB=AC implies B=C.Ch. 1.1 - 38. Prove or disprove that .
Ch. 1.1 - Prove or disprove that (AB)=(A)(B).Ch. 1.1 - 40. Prove or disprove that .
Ch. 1.1 - Express (AB)(AB) in terms of unions and...Ch. 1.1 - 42. Let the operation of addition be defined on...Ch. 1.1 - 43. Let the operation of addition be as defined in...Ch. 1.2 - Label each of the following statements as either...Ch. 1.2 - Label each of the following statements as either...Ch. 1.2 - Label each of the following statements as either...Ch. 1.2 - Label each of the following statements as either...Ch. 1.2 - Label each of the following statements as either...Ch. 1.2 - True or False
Label each of the following...Ch. 1.2 - Label each of the following statements as either...Ch. 1.2 - Label each of the following statements as either...Ch. 1.2 - Label each of the following statements as either...Ch. 1.2 - 1. For the given sets, form the Cartesian...Ch. 1.2 - For each of the following mapping, state the...Ch. 1.2 - 3. For each of the following mappings, write out ...Ch. 1.2 - For each of the following mappings f:ZZ, determine...Ch. 1.2 - 5. For each of the following mappings, determine...Ch. 1.2 - 6. For the given subsets and of Z, let and...Ch. 1.2 - 7. For the given subsets and of Z, let and...Ch. 1.2 - 8. For the given subsets and of Z, let and...Ch. 1.2 - For the given subsets A and B of Z, let f(x)=2x...Ch. 1.2 - For each of the following parts, give an example...Ch. 1.2 - For the given f:ZZ, decide whether f is onto and...Ch. 1.2 - 12. Let and . For the given , decide whether is...Ch. 1.2 - 13. For the given decide whether is onto and...Ch. 1.2 - 14. Let be given by
a. Prove or disprove that ...Ch. 1.2 - 15. a. Show that the mapping given in Example 2...Ch. 1.2 - 16. Let be given by
a. For , find and .
b. ...Ch. 1.2 - 17. Let be given by
a. For find and.
b. For...Ch. 1.2 - 18. Let and be defined as follows. In each case,...Ch. 1.2 - Let f and g be defined in the various parts of...Ch. 1.2 - In Exercises 20-22, Suppose and are positive...Ch. 1.2 - In Exercises 20-22, Suppose and are positive...Ch. 1.2 - In Exercises 20-22, Suppose and are positive...Ch. 1.2 - Let a and b be constant integers with a0, and let...Ch. 1.2 - 24. Let, where and are nonempty.
Prove that for...Ch. 1.2 - 25. Let, where and are non empty, and let and ...Ch. 1.2 - 26. Let and. Prove that for any subset of T of...Ch. 1.2 - 27. Let , where and are nonempty. Prove that ...Ch. 1.2 - 28. Let where and are nonempty. Prove that ...Ch. 1.3 - Label each of the following statements as either...Ch. 1.3 - Label each of the following statements as either...Ch. 1.3 - Label each of the following statements as either...Ch. 1.3 - Label each of the following statements as either...Ch. 1.3 - True or False
Label each of the following...Ch. 1.3 - Label each of the following statements as either...Ch. 1.3 - For each of the following pairs and decide...Ch. 1.3 - For each pair given in Exercise 1, decide whether ...Ch. 1.3 - Let . Find mappings and such that.
Ch. 1.3 - Give an example of mappings and such that one of...Ch. 1.3 - Give an example of mapping and different from...Ch. 1.3 - 6. a. Give an example of mappings and , different...Ch. 1.3 - 7. a. Give an example of mappings and , where is...Ch. 1.3 - Suppose f,g and h are all mappings of a set A into...Ch. 1.3 - Find mappings f,g and h of a set A into itself...Ch. 1.3 - Let g:AB and f:BC. Prove that f is onto if fg is...Ch. 1.3 - 11. Let and . Prove that is one-to-one if is...Ch. 1.3 - Let f:AB and g:BA. Prove that f is one-to-one and...Ch. 1.4 - True or False
Label each of the following...Ch. 1.4 - True or False
Label each of the following...Ch. 1.4 - Label each of the following statements as either...Ch. 1.4 - True or False
Label each of the following...Ch. 1.4 - True or False Label each of the following...Ch. 1.4 - True or False
Label each of the following...Ch. 1.4 - True or False
Label each of the following...Ch. 1.4 - True or False
Label each of the following...Ch. 1.4 - True or False Label each of the following...Ch. 1.4 - 1. Decide whether the given set is closed with...Ch. 1.4 - In each part following, a rule that determines a...Ch. 1.4 - 3. Let be a set of three elements given by . In...Ch. 1.4 - 4. Let be a set of three elements given by . In...Ch. 1.4 - 5. Let be the set of four elements given by with...Ch. 1.4 - Let S be the set of four elements given by S={...Ch. 1.4 - 7. Prove or disprove that the set of nonzero...Ch. 1.4 - 8. Prove or disprove that the set of all odd...Ch. 1.4 - 9. The definition of an even integer was stated in...Ch. 1.4 - 10. Prove or disprove that the set of all nonzero...Ch. 1.4 - Prove or disprove that the set B={ z3|zZ } is...Ch. 1.4 - 12. Prove or disprove that the set of non zero...Ch. 1.4 - Assume that is an associative binary operation on...Ch. 1.4 - Assume that is a binary operation on a non empty...Ch. 1.4 - 15. Let be a binary operation on the non empty...Ch. 1.4 - Assume that is an associative binary operation on...Ch. 1.5 - True or False Label each of the following...Ch. 1.5 - True or False Label each of the following...Ch. 1.5 - True or False
Label each of the following...Ch. 1.5 - For each of the following mappings exhibit a...Ch. 1.5 - 2. For each of the mappings given in Exercise 1,...Ch. 1.5 - 3. If is a positive integer and the set has ...Ch. 1.5 - 4. Let , where is nonempty. Prove that a has...Ch. 1.5 - Let f:AA, where A is nonempty. Prove that f a has...Ch. 1.5 - 6. Prove that if is a permutation on , then is a...Ch. 1.5 - Prove that if f is a permutation on A, then...Ch. 1.5 - 8. a. Prove that the set of all onto mappings from...Ch. 1.5 - Let f and g be permutations on A. Prove that...Ch. 1.5 - 10. Let and be mappings from to. Prove that if is...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - True or False
Label each of the following...Ch. 1.6 - Label each of the following statements as either...Ch. 1.6 - Write out the matrix that matches the given...Ch. 1.6 - 2. Perform the indicated operations, if...Ch. 1.6 - 3. Perform the following multiplications, if...Ch. 1.6 - Let A=[aij]23 where aij=i+j, and let B=[bij]34...Ch. 1.6 - 5. Show that the matrix equation is equivalent to...Ch. 1.6 - 6. Write a single matrix equation of the form ...Ch. 1.6 - Let ij denote the Kronecker delta: ij=1 if i=j,...Ch. 1.6 - Let S be the set of four matrices S={I,A,B,C},...Ch. 1.6 - 9. Find two square matrices and such that.
Ch. 1.6 - Find two nonzero matrices A and B such that AB=BA.Ch. 1.6 - 11. Find two nonzero matrices and such that.
Ch. 1.6 - 12. Positive integral powers of a square matrix...Ch. 1.6 - For the matrices in Exercise 12, evaluate (A+B)2...Ch. 1.6 - Assume that A1 exists and find a solution X to...Ch. 1.6 - 15. Assume that are in and with and invertible....Ch. 1.6 - a. Prove part d of Theorem 1.30. b. Prove part e...Ch. 1.6 - a. Prove part a. of Theorem 1.34. b. Prove part b....Ch. 1.6 - Prove part b of Theorem 1.35.
Theorem 1.35 ...Ch. 1.6 - Let a and b be real numbers and A and B elements...Ch. 1.6 - Prove that if then.
Ch. 1.6 - Suppose that A is an invertible matrix over and O...Ch. 1.6 - Let be the set of all elements of that have one...Ch. 1.6 - Prove that the set S={[abba]|a,b} is closed with...Ch. 1.6 - Prove or disprove that the set of diagonal...Ch. 1.6 - Let A and B be square matrices of order n over...Ch. 1.6 - Let and be square matrices of order over ....Ch. 1.6 - A square matrix A=[aij]n with aij=0 for all ij is...Ch. 1.6 - Let a,b,c,andd be real numbers. If adbc0, show...Ch. 1.6 - Let A=[abcd] over . Prove that if adbc=0, then A...Ch. 1.6 - Let be elements of where is not a zero matrix....Ch. 1.6 - Let A,BandC be square matrices of order n over ....Ch. 1.6 - Let A and B be nn matrices over such that A1 and...Ch. 1.7 - Label each of the following statements as either...Ch. 1.7 - True or False
Label each of the following...Ch. 1.7 -
True or False
Label each of the following...Ch. 1.7 - Label each of the following statements as either...Ch. 1.7 - True or False
Label each of the following...Ch. 1.7 - Label each of the following statements as either...Ch. 1.7 - For determine which of the following relations...Ch. 1.7 - 2. In each of the following parts, a relation is...Ch. 1.7 - a. Let R be the equivalence relation defined on Z...Ch. 1.7 - 4. Let be the relation “congruence modulo 5”...Ch. 1.7 - 5. Let be the relation “congruence modulo ”...Ch. 1.7 - In Exercises 610, a relation R is defined on the...Ch. 1.7 - In Exercises 610, a relation R is defined on the...Ch. 1.7 - In Exercises 610, a relation R is defined on the...Ch. 1.7 - In Exercises 610, a relation R is defined on the...Ch. 1.7 - In Exercises , a relation is defined on the set ...Ch. 1.7 - Let be a relation defined on the set of all...Ch. 1.7 - Let and be lines in a plane. Decide in each case...Ch. 1.7 - 13. Consider the set of all nonempty subsets of ....Ch. 1.7 - In each of the following parts, a relation is...Ch. 1.7 - Let A=R0, the set of all nonzero real numbers, and...Ch. 1.7 - 16. Let and define on by if and only if ....Ch. 1.7 - In each of the following parts, a relation R is...Ch. 1.7 - Let (A) be the power set of the nonempty set A,...Ch. 1.7 - For each of the following relations R defined on...Ch. 1.7 - Give an example of a relation R on a nonempty set...Ch. 1.7 - 21. A relation on a nonempty set is called...Ch. 1.7 - A relation R on a nonempty set A is called...Ch. 1.7 - A relation R on a nonempty set A is called...Ch. 1.7 - For any relation on the nonempty set, the inverse...Ch. 1.7 - 25. Let , , and . Write out and .
Ch. 1.7 - 26. Let , , and . Write out and .
Ch. 1.7 - Prove Theorem 1.40: If is an equivalence relation...Ch. 1.7 - 28. Let , and . Define the relation R on A by if...Ch. 1.7 - 29. Suppose , , represents a partition of the...Ch. 1.7 - Suppose thatis an onto mapping from to. Prove that...

Find more solutions based on key concepts

Show solutions For Problems 3-11, simplify each numerical expression. 5(13)3(12)+7(23)+1

Intermediate Algebra

Critical Thinking Consider the following events for a driver selected at random from the general population: A ...

Understanding Basic Statistics

Use the probability demonstrator, in the left margin, to work Excursion. How many routes can a ball take as it ...

Mathematical Excursions (MindTap Course List)

Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the...

Single Variable Calculus

Solve each equation in Exercises 107120 for x, rounding your answer to four significant digits where necessary....

Applied Calculus

The equation (x + 1)2 5(x + 1) + 6 = 0 is __________ of type. To solve the equation, we set W = __________. Th...

Precalculus: Mathematics for Calculus (Standalone Book)

Solve each equation in Exercises 107120 for x, rounding your answer to four significant digits where necessary....

Finite Mathematics

If an equation of the tangent tine to the curve y = f(x) at the point where a = 2 is y = 4x 5, find f(2) and f...

Single Variable Calculus: Early Transcendentals, Volume I

Use the percentage method of income tax calculation to complete the following payroll roster. Employee Marital ...

Contemporary Mathematics for Business & Consumers

Let X be the temperature in C at which a certain chemical reaction takes place, and let Y be the temperature in...

Probability and Statistics for Engineering and the Sciences

Find the most general antiderivative of the function. Check your answer by differentiation. f(x)=x23+xx

Calculus (MindTap Course List)

Let tan=3 with in QI and find the following. sec2

Trigonometry (MindTap Course List)

Finding Values In Exercises 23 and 24, find the value(s) of y such that the distance between the points is 8. (...

Calculus: An Applied Approach (MindTap Course List)

In Exercises 1 to 6, which property justifies the conclusion of the statement? If x5=3, then x=15.

Elementary Geometry For College Students, 7e

Fill in the blanks. 7. a. An equation of the line passing through the point P(x1, y1) and having slope m is ___...

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

Rectangular-to-Polar Conversion In Exercises 25-34, convert the rectangular equation to polar form and sketch i...

Calculus: Early Transcendental Functions

SOC A scale measuring prejudice has been administered to a large sample of respondents. The distribution of sco...

Essentials Of Statistics

Expand each expression in Exercises 122. (x+yxy)2

Finite Mathematics and Applied Calculus (MindTap Course List)

For the following set at scores: 1. Construct a frequency distribution table to organize the scores. 2. Draw a ...

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

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or gi...

Calculus: Early Transcendentals

a. Solve for the indicated. b. Then substitute the given values to find the value of the indicated letter (use ...

Elementary Technical Mathematics

Consider the points P such that the distance from P to A( 1, 5, 3) is twice the distance from P to B(6, 2, 2). ...

Multivariable Calculus

One sample has SS=60 and a second sample has SS=48 . a. If n=7 for both samples, find each of the sample varian...

Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the definite integrals in Problems 1-32.

Mathematical Applications for the Management, Life, and Social Sciences

The graph of the concentration function c(t) is shown after a 7-mg injection of dye into a heart. Use Simpsons ...

Single Variable Calculus: Early Transcendentals

Evaluating a Definite Integral In Exercises 538, evaluate the definite integral. Use a graphing utility to veri...

Calculus: Early Transcendental Functions (MindTap Course List)

Errors and Eulers Method The exact solution of the differential equation y=2y, where y(0)=4, is y=4e2x a) Use a...

Calculus of a Single Variable

Formulate but do not solve each of the following exercises as a linear programming problem. You will be asked t...

Finite Mathematics for the Managerial, Life, and Social Sciences

If 4 is a critical number for f and f′(x) < 0 for x < 4 and f′(x) > 0 for x > 4, then:
f has a local maximum at...

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

In ABCD, AD=5 and DC=9. If the altitude from vertex D to AB has length 4that is, DE=4, find the length of EB. _...

Elementary Geometry for College Students

Internet addiction has been described as excessive and uncontrolled Internet use. The authors of the paper Gend...

Introduction To Statistics And Data Analysis

True or False:
If dz exists at (x, y), then z = f(x, y) is differentiable at (x, y).

Study Guide for Stewart's Multivariable Calculus, 8th

You should be able to complete these vocabulary ad concept statements before you proceed to the practice exerci...

College Algebra (MindTap Course List)

The Information Systems Audit and Control Association surveyed office workers tolearn about the anticipated usa...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe how some behaviors can be explained by clichés, such as “You cant teach an old dog new tricks or “You ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Think About It Consider the equation x29+y24=1 (a) Use a graphing utility to graph the equation. (b) Write the ...

Calculus (MindTap Course List)

Write a multiple regression equation that can be used to analyze the data for a two-factorial design with two l...

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

Finding Partial Derivatives Using Technology In Exercises 87-90, use a computer algebra system to find the firs...

Multivariable Calculus

Two studies (Hughes, Cutting, Hughes et al., 2002) have demonstrated a new observational technique for assessi...

Research Methods for the Behavioral Sciences (MindTap Course List)

Solve these examples of combined operations. Round the answers to 2 decimal places where necessary. 23. 81.0712...

Mathematics For Machine Technology

Doppler Effect Motion towards or away from us distorts the pitch of sound, and it also distorts the wavelength ...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Count Chocula Cereal. Filling boxes with consistent amounts of its cereals is critical to General Millss succes...

Essentials Of Statistics For Business & Economics

In Problems 16 proceed as in Example 1 to find a particular solution yp(x) of the given differential equation i...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Classify each argument as deductive and inductive. a.1. Hitchcocks Psycho is a suspenseful movie. 2. Hitchcocks...

Mathematics: A Practical Odyssey

Justify formula (4.5.1) for general values of DayT and N.

Discrete Mathematics With Applications

33. Consider a regression study involving a dependent variable y, a quantitative independent variable x1, and a...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Solve e2x7ex+12=0.

College Algebra

Use the following information to answer the next ten exercises. A customer service representative must spend di...

Introductory Statistics

For the following exercises, for each polynomial, a. find the degree; b. find the zeros, if any; c. find the y ...

Calculus Volume 1

Find the derivative. 457. ddx1In(x)(4t+et)dt

Calculus Volume 2