BuyFind*arrow_forward*

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 8.5, Problem 8ES

Textbook Problem

Define a relation *R *on *Z*, the set of all integers as follows: For every

Is *R *a partial order relation? Prove or give a counterexample.

Discrete Mathematics With Applications

Show all chapter solutions

Ch. 8.1 - If R is a relation from A to B, xA , and yB , the...Ch. 8.1 - If R is a relation from A to B, xA and yB , the...Ch. 8.1 - If R is a relation from A to B, xA , and yB , then...Ch. 8.1 - A relation on a set A is a realtion _______to...Ch. 8.1 - If R is a relation on a set A, the directed graph...Ch. 8.1 - As in Example 8.1.2, the congruence modulo 2...Ch. 8.1 - Prove that for all integers m and n,m-n is even...Ch. 8.1 - The congruence modulo 3 relation, T, is defined...Ch. 8.1 - Define a relation P on Z as follows: For every...Ch. 8.1 - Let X={a,b,c} . Recall that P(X) is the power set...

Ch. 8.1 - Let X={a,b,c}. Define a relation J on P(X) as...Ch. 8.1 - Define a relation R on Z as follows: For all...Ch. 8.1 - Let A be the set of all string of a’s and b’s of...Ch. 8.1 - Let A be the set of all strings of 0’s, 1’s, and...Ch. 8.1 - Let A={3,4,5} and B={4,5,6} and let R be the “less...Ch. 8.1 - Let A={3,4,5} and B={4,5,6} and let S be the...Ch. 8.1 - Suppose a function F:XY is one-to-one but not...Ch. 8.1 - Draw the directed graphs of the relations defined...Ch. 8.1 - Draw the directed graphs of the relations defined...Ch. 8.1 - Draw the directed graphs of the relations defined...Ch. 8.1 - Draw the directed graphs of the relations defined...Ch. 8.1 - Draw the directed graphs of the relations defined...Ch. 8.1 - Draw the directed graphs of the relations defined...Ch. 8.1 - Exercises 19-20 refer to unions and intersections...Ch. 8.1 - Exercises 19—20 refer to unions and intersections...Ch. 8.1 - Define relation R and S on R as follows:...Ch. 8.1 - Define relations R and S on R as follows:...Ch. 8.1 - Define relations R and S on R as follows:...Ch. 8.1 - In Example 8.17 consider the query SELECT...Ch. 8.2 - For a relation R on a set A to be reflexive means...Ch. 8.2 - For a relation R on a set A to be symmetric means...Ch. 8.2 - For a relation R on a set A to be transitive means...Ch. 8.2 - To show that a relation R on an infinite set A is...Ch. 8.2 - To show that a relation R on an infinite set A is...Ch. 8.2 - To show that a relation R on an infinite set A is...Ch. 8.2 - To show that a relation R on a set A is not...Ch. 8.2 - To show that a relation R on a set not symmentric,...Ch. 8.2 - To show that a relation R on a set A is not...Ch. 8.2 - Given a relation R on a set A, the transitive...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 1-8, a number of relations are defined on the...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9—33, determine whether the given relation is...Ch. 8.2 - In 9—33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given is reflexive...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9—33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 9-33, determine whether the given relation is...Ch. 8.2 - In 34-36, assume that R is a relation on a et A....Ch. 8.2 - In 34-36, assume that R is a relation on a et A....Ch. 8.2 - In 34-36, assume that R is a relation on a et A....Ch. 8.2 - In 37-42, assume that R and S are relations on set...Ch. 8.2 - In 37-42, assume that R and S are relations on a...Ch. 8.2 - In 37-42, assume that R and S are relations on set...Ch. 8.2 - In 37-42, assume that R and S are relations on set...Ch. 8.2 - In 37-42, assume that R and S are relations on a...Ch. 8.2 - In 37-42, assume that R and S are relations on a...Ch. 8.2 - In 43-50, the following definitions are used: A...Ch. 8.2 - In 43-50, the following definitions are used: A...Ch. 8.2 - In 43-50, the following definitions are used: A...Ch. 8.2 - In 43-50, the following definitions are used: A...Ch. 8.2 - In 43-50, the following definitions are used: A...Ch. 8.2 - In 43-50, the following definitions are used: A...Ch. 8.2 - In 43-50, the following definitions are used: A...Ch. 8.2 - In 43-50, the following definitions are used: A...Ch. 8.2 - In 51—53, R, S, and T are relations defined on...Ch. 8.2 - In 51—53, R, S, and T are relations defined on...Ch. 8.2 - In 51-53, R,S, and T are relations defined...Ch. 8.2 - Write a computer algorithm to test whether a...Ch. 8.2 - Write a computer algorithm to test whether a...Ch. 8.2 - Write a computer algorithm to test whether a...Ch. 8.3 - For a relation on a set to be an equivalence...Ch. 8.3 - The notation m=n(modd) is...Ch. 8.3 - Given an equivalence relation R on a set A and...Ch. 8.3 - If A is a set, R is an equivalence relation A, and...Ch. 8.3 - If A is a set and R is an equivalence relation on...Ch. 8.3 - Let A=Z(Z{0}) , and define a relation R on A by...Ch. 8.3 - Suppose that S={a,b,c,d,e} and R is a relation on...Ch. 8.3 - Each of the following partitions of {0,1,2,3,4}...Ch. 8.3 - In each of 3-6, the relation R is an equivalence...Ch. 8.3 - In each of 3—6, the relation R is an equivalence...Ch. 8.3 - In each of 3-6, the relation R is an equivalence...Ch. 8.3 - In each of 3-6, the relation R is an equivalence...Ch. 8.3 - In each of 7-14, the relation R is an equivalence...Ch. 8.3 - In each of 7-14, the relation R is an equivalence...Ch. 8.3 - In each of 7-14, the relation R is an equivalence...Ch. 8.3 - In each of 7-14, relation R is an equivalence...Ch. 8.3 - In each of 7-14, relation R is an equivalence...Ch. 8.3 - In each of 7-14, relation R is an equivalence...Ch. 8.3 - In each of 7-14, the relation R is an equivalence...Ch. 8.3 - In each of 7—14, the relation R is an equivalence...Ch. 8.3 - Determine which of the following congruence...Ch. 8.3 - Let R be the relation of congruence modulo 3....Ch. 8.3 - Prove that for all integers m and n,m=n (mod 3)...Ch. 8.3 - Give an example of two sets that are distinct but...Ch. 8.3 - In 19-31, (1) prove that the relation is an...Ch. 8.3 - In 19—31, (1) prove that the relation is an...Ch. 8.3 - In 19—31, (1) prove that the relation is an...Ch. 8.3 - In 19-31, (1) prove that the relation is an...Ch. 8.3 - In 19-31, (1) prove that the relation is an...Ch. 8.3 - In 19-31. (1) prove that the relation is an...Ch. 8.3 - In 19-31,(1) prove that the relation is an...Ch. 8.3 - In 19-31,(1) prove that the relation is an...Ch. 8.3 - In 19-31,(1) prove that the relation is an...Ch. 8.3 - In 19-31,(1) prove that the relation is an...Ch. 8.3 - In 19-31, (1) prove that the relation is an...Ch. 8.3 - In 19-31, (1) prove that the relation is an...Ch. 8.3 - In 19—31, (1) prove that the relation is an...Ch. 8.3 - Let A be the set of all straight lines in the...Ch. 8.3 - Let A be the set of points in the rectangle...Ch. 8.3 - The documentation for the computer language Java...Ch. 8.3 - Find an additional representative circuit for the...Ch. 8.3 - Let R be an equivalence relation on a set A. Prove...Ch. 8.3 - Let R be an equivalence relation on a set A. Prove...Ch. 8.3 - Let R be an equivalence relation on a set A. Prove...Ch. 8.3 - Let R be an equivalence relation on a set A. Prove...Ch. 8.3 - Let R be an equivalence relation on a set A. Prove...Ch. 8.3 - Let R be an equivalence relation on s set A. Prove...Ch. 8.3 - Let R be the relation defined in Example 8.3.12....Ch. 8.3 - In Example 8.3.12, define operations of addition...Ch. 8.3 - Let A=Z+Z+ . Define a relation R on A as follows:...Ch. 8.3 - The following argument claims to prove that the...Ch. 8.3 - Let R be a relation on a set A and suppose R is...Ch. 8.3 - Refer to the quote at the beginning of this...Ch. 8.4 - When letters of the alphabet are encrypted using...Ch. 8.4 - If a,b, and n are integers with n1 , all of the...Ch. 8.4 - If a, b. c, d, m, and n arc integers with n1 and...Ch. 8.4 - If a, n, and k are positive integers with n1 , an...Ch. 8.4 - To express a greatest common divisor of two...Ch. 8.4 - To find an inverse for a positive integer a modulo...Ch. 8.4 - TO encrypt a message M using RSA cryptography with...Ch. 8.4 - Euclid’s lemma says that for all integers a, b,...Ch. 8.4 - Fermat’s little theorem says that if p is any...Ch. 8.4 - The crux of the proof that the RSA cipher words is...Ch. 8.4 - Use the Caesar cipher to encrypt the message WHERE...Ch. 8.4 - Use the Caesar cipher to encrypt the message AN...Ch. 8.4 - Let a=25,b=19, and n=3. Verify that 3(2519) ....Ch. 8.4 - Let a=68, b=33, and n=7. Verify that 7|(68-33)....Ch. 8.4 - Prove the transitivity of modular congruence. That...Ch. 8.4 - Prove that the distinct equivalence classes of the...Ch. 8.4 - Verify the following statements. 128=2(mod7) and...Ch. 8.4 - Verify the following statements. 45=3 (mod 6) and...Ch. 8.4 - In 9-11, prove each of the given statements,...Ch. 8.4 - In 9-11, prove each of the given statements,...Ch. 8.4 - In 9-11, prove each of the given statements,...Ch. 8.4 - Prove that for every integer n0,10n=1(mod9) . Use...Ch. 8.4 - a. Prove that for every integer n1 ,...Ch. 8.4 - Use the technique of Example 8.4.4 to find...Ch. 8.4 - Use the result of exercise 14 an d the technique...Ch. 8.4 - In 16-18, use the techniques of Example 8.4.4 and...Ch. 8.4 - In 16-18, use the techniques of Example 8.4.4 and...Ch. 8.4 - In 16-18, use the techniques of Example 8.4.4 and...Ch. 8.4 - In 19-24, use the RSA cipher from Examples 8.4.9...Ch. 8.4 - In 19-24, use the RSA cipher from Examples 8.4.9...Ch. 8.4 - In 19-24, use the RSA cipher from Examples 8.4.9...Ch. 8.4 - In 19-24, use the RSA cipher from Examples 8.4.9...Ch. 8.4 - In 19-24, use the RSA cipher from Examples 8.4.9...Ch. 8.4 - In 19-24, use the RSA cipher from Examples 8.4.9...Ch. 8.4 - Use Theorem 5.2.2 to prove that if a and n are...Ch. 8.4 - In 26 and 27, use the extended Euclidean algorithm...Ch. 8.4 - In 26 and 27, use the extended Euclidean algorithm...Ch. 8.4 - In 28 and 29, for the given values of A and B,...Ch. 8.4 - In 28 and 29, for the given values of A and B,...Ch. 8.4 - Finish the proof of Theorem 8.4.5 by proving that...Ch. 8.4 - Find an inverse for 210 modulo 13. Find appositive...Ch. 8.4 - Find an inverse for 41 modulo 660. Find the least...Ch. 8.4 - Use Theorem 8.4.5to prove that for all integers a,...Ch. 8.4 - Give a counterexample to show that the statement...Ch. 8.4 - Corollary 8.4.7 guarantees the existence of an...Ch. 8.4 - In 36,37,39 and 40, use the RSA cipher with public...Ch. 8.4 - In 36,37,39 and 40, use the RSA cipher with public...Ch. 8.4 - Find the least positive inverse for 43 modulo 660.Ch. 8.4 - In 36,37,39 and 40, use the RSA cipher with public...Ch. 8.4 - In 36,37,39 and 40, use the RSA cipher with public...Ch. 8.4 - a. Use mathematical induction and Euclid’s lemma...Ch. 8.4 - According to Fermat’s little theorem, if p is a...Ch. 8.4 - Fermat’s little theorem can be used to show that a...Ch. 8.5 - For a relation R on a set A on a set to be...Ch. 8.5 - To show that a relation R on an infinite set A is...Ch. 8.5 - To show that a relation R on a set A is not...Ch. 8.5 - To construct a Hasse diagram for a partial order...Ch. 8.5 - If A is a set that is partially odereed with...Ch. 8.5 - A relation on a set A is a total order if, and...Ch. 8.5 - If A a set that is partially ordered with respect...Ch. 8.5 - Let A be a set that is partially order with...Ch. 8.5 - Given a set A that is partially ordered with...Ch. 8.5 - PERT and CPM are used to produces efficient_____Ch. 8.5 - Each of the following is a relation on {0,1,2,3}...Ch. 8.5 - Let P be the set of all people in the world and...Ch. 8.5 - Let S be the set of all strings of a’s and b’s....Ch. 8.5 - Let R be the “less than” relation on R, the set of...Ch. 8.5 - Let R be the set of all real numbers and define a...Ch. 8.5 - Let P be the set of all people who have ever lived...Ch. 8.5 - Define a relation R on Z, the set of all integers...Ch. 8.5 - Define a relation R on Z, the set of all integers...Ch. 8.5 - Define a relation R on R, the set of all real...Ch. 8.5 - Suppose R and S are antisymmetric relations on a...Ch. 8.5 - Let A={a,b}, and supposeAhas the partial order...Ch. 8.5 - Prove Theorem 8.5.1Ch. 8.5 - Let A={a,b} . Describe all partial order relations...Ch. 8.5 - Let A={a,b,c}. Describe all partial order...Ch. 8.5 - Suppose a relation R on a set A is reflexive,...Ch. 8.5 - Consider the “divides” relation on each of the...Ch. 8.5 - Consider the “sbset” relation on P(S) for each of...Ch. 8.5 - Let S={0,1} and consider the partial order...Ch. 8.5 - Let S={0,1} and consider the partial order...Ch. 8.5 - Let S={0,1} and consider the partial order...Ch. 8.5 - Consider the “divides” relation defined on the set...Ch. 8.5 - In 22-29, find all greatest, least, maximal, and...Ch. 8.5 - In 22-29, find all greatest, least, maximal, and...Ch. 8.5 - In 22-29, find all greatest, least, maximal, and...Ch. 8.5 - In 22-29, find all greatest, least, maximal, and...Ch. 8.5 - In 22—29, find all greatest, least, maximal, and...Ch. 8.5 - In 22—29, find all greatest, least, maximal, and...Ch. 8.5 - In 22—29, find all greatest, least, maximal, and...Ch. 8.5 - In 22—29, find all greatest, least, maximal, and...Ch. 8.5 - Each of the following sets is partially ordered...Ch. 8.5 - Let A={a,b,c,d} , and let R be the relation...Ch. 8.5 - Let A={a,b,c,d} , and let R be the relation...Ch. 8.5 - Consider the set A={12,24,48,3,9} ordered by the...Ch. 8.5 - Suppose that R is a partial order relation on a...Ch. 8.5 - The set P({w,x,y,z}) is partially ordered with...Ch. 8.5 - The set A={2,4,3,6,12,18,24} is partially ordered...Ch. 8.5 - Find a chain of length 2 for the relation defined...Ch. 8.5 - Prove that a partially ordered set is totally...Ch. 8.5 - Suppose that A is a totally ordered set. Use...Ch. 8.5 - Prove that a nonempty, finite, partially ordered...Ch. 8.5 - Prove that a finite, partially ordered set has At...Ch. 8.5 - Draw a Hasse diagram for a partially ordered set...Ch. 8.5 - Draw a Hasse diagram for a partially ordered set...Ch. 8.5 - Use the algorithm given in the text find a...Ch. 8.5 - Use the algorithm given in the text to find a...Ch. 8.5 - Use the algorithm given in the text to find a...Ch. 8.5 - Use the algorithm given in the text to find a...Ch. 8.5 - Use the algorithm given in the text to find a...Ch. 8.5 - Refer to the prerequisite structure show in Figure...Ch. 8.5 - A set S of jobs can be ordered by writing x_y to...Ch. 8.5 - Suppose the tasks described in Example 8.5.12...

Find more solutions based on key concepts

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

Finite Mathematics

Determine whether the congruence is true or false. 885mod9

Mathematical Excursions (MindTap Course List)

Write an equation for each of the following problems, solve for the unknown, and check. A hole is countersunk a...

Mathematics For Machine Technology

In Exercise 16, find the value of the probability of the standard normal variable Z corresponding to the shaded...

Finite Mathematics for the Managerial, Life, and Social Sciences

11. If , find the following.
(a) (b) (c) (d)

Mathematical Applications for the Management, Life, and Social Sciences

Global Air Lines has contracted with a tour group to transport a minimum of 1,600 first-class passengers and 4,...

Mathematics: A Practical Odyssey

Solve each equation by factoring: 5x26x=0

Elementary Technical Mathematics

Determining Continuity In Exercises 111122, describe the interval(s) on which the function is continuous. Expla...

Calculus: An Applied Approach (MindTap Course List)

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. 1(x+y...

Finite Mathematics and Applied Calculus (MindTap Course List)

A company uses three different assembly linesA1, A2, and A3to manufacture a particular component. Of those manu...

Probability and Statistics for Engineering and the Sciences

Disposable Income Economists define the disposable annual income for an individual by the equation D = (1 r)T,...

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

In Exercises 15-22, find the equation of the specified line. With slope 4 crossing 2x3y=6 at its x-intercept

Applied Calculus

A binomial probability distribution has p = .20 and n = 100. a. What are the mean and standard deviation? b. Is...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Explain the difference among the terms research strategy, research design, and research procedure.

Research Methods for the Behavioral Sciences (MindTap Course List)

A table of values of an increasing function f is shown. Use the table to find lower and upper estimates for 103...

Single Variable Calculus

Calculate the interest, purchase price, and effective interest rate of the following Treasury bill (T-bill) pur...

Contemporary Mathematics for Business & Consumers

Label each of the following statements as either true or false.
Every decimal representation of a real number t...

Elements Of Modern Algebra

Sue and Daves semicircular driveway is to be resealed, and then flowers are to be planted on either side. aWhat...

Elementary Geometry for College Students

Calculate the double integral. 34. R11+x+ydA,R=[1,3][1,2]

Multivariable Calculus

Find the linear velocity of a point moving with uniform circular motion, if the point covers a distance s in th...

Trigonometry (MindTap Course List)

A triangle has sides that measure 15 cm, 20 cm, and 25 cm. Find the exact volume of the solid of revolution for...

Elementary Geometry For College Students, 7e

Relative Extrema and Points of Inflection In Exercises 71-78, find the relative extrema and the points of infle...

Calculus (MindTap Course List)

Rate of growth A small business predicts sales according to a straight-line method. If sales were 50,000 in the...

College Algebra (MindTap Course List)

Evaluating a Line Integral Using Greens TheoremIn Exercises 1524, use Greens Theorem to evaluate the line integ...

Multivariable Calculus

In problem 13 in Chapter 17, we Discussed a study by Loftus and Palmer (1974) examining how different phrasing ...

Statistics for The Behavioral Sciences (MindTap Course List)

The pursuit of a higher education degree in business is now international. A survey shows that more and more As...

Essentials Of Statistics For Business & Economics

DISCUSS: Products of Even and Odd Functions Answer the same questions as in Exercise 102, except this time cons...

Precalculus: Mathematics for Calculus (Standalone Book)

True or False:
If R is a rectangular region in the plane, then

Study Guide for Stewart's Multivariable Calculus, 8th

The spotlight effect refers to overestimating the extent to which others notice your appearance or behavior, es...

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

Find the vertex, focus, and directrix of the parabola and sketch its graph. 6. (y 2)2 = 2x + 1

Calculus: Early Transcendentals

For Problems 51-78, simplify each of the numerical expressions. Objective 3 [7+2355]8

Intermediate Algebra

Matt Kenseth won the 2012 Daytona 500, the most important race of the NASCAR season. His win was no surprise be...

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

A function f is defined by f(x)=limnx2n1x2n+1 Where is f continuous?

Calculus (MindTap Course List)

Horizontal and Vertical Tangency In Exercises 35-42, find all points (if any) of horizontal and vertical tangen...

Calculus of a Single Variable

Reminder Round all answer to two decimal places unless otherwise indicated. 4.Triangle Find the area of the sha...

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

Critical Thinking A personnel office is gathering data regarding working conditions. Employees are givena list ...

Understanding Basic Statistics

Use the guidelines of this section to sketch the curve. y = x + cos x

Single Variable Calculus: Early Transcendentals, Volume I

Finding Points of Intersection Using Technology In Exercises 63-66, use a graphing utility to find the points o...

Calculus: Early Transcendental Functions (MindTap Course List)

Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition...

Single Variable Calculus: Early Transcendentals

Finding an Inverse Function In Exercises 31-38, (a) find the inverse function of f, (b) graph f and f1 on the s...

Calculus: Early Transcendental Functions

If a distribution of test scores is normal, with a mean of 78 and a standard deviation of 11, what percentage o...

Essentials Of Statistics

Based on a study of 2 121 children between the ages of 1 and 4, researchers at the Medical College of Wisconsin...

Introduction To Statistics And Data Analysis

For f(x) = 10x2, f′(3) = _____.
10
20
30
60

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

A researcher finds that college students are more anxious near final exams in December than at the beginning of...

Research Methods for the Behavioral Sciences (MindTap Course List)

For the following exercises, use composition to determine which pairs of functions are inverses. 203. f(x)=1x1,...

Calculus Volume 1

Suppose that 04f(x)dx=5 and 02f(x)dx=3 , and 04g(x)dx=1 and 02g(x)dx=2 . In the following exercises, compute th...

Calculus Volume 2

In Problems 1-18 solve each differential equation by variation of parameters. 5. y + y = cos2 x

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

Adding or Subtracting Polynomials In Exercises 17-24, add or subtract and write the result in standard form. 2x...

College Algebra

4. The variance in drug weights is critical in the pharmaceutical industry. For a specific drug, with weights m...

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