Math

Discrete Mathematics With Applicationsa. Define f : Z → Z by the rule f ( n ) = 2 n , for every integer n . (i) Is f one-to-one? Prove or give a counterexample. (ii) Is f onto? Prove or give a counterexample. b. Let 2Z denote the set of all even integers. That is, 2 Z = { n ∈ Z | n = 2 k , for some integer k } . Define h : Z → 2 Z by the rule h ( n ) = 2 n , for each integer n . Is h onto? Prove or give a counterexample.BuyFind*arrow_forward*

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 7.2, Problem 10ES

Textbook Problem

a. Define
*n*.

(i) Is *f *one-to-one? Prove or give a counterexample.

(ii) Is *f *onto? Prove or give a counterexample.

b. Let 2Z denote the set of all even integers. That is,
*n*. Is *h *onto? Prove or give a counterexample.

Discrete Mathematics With Applications

Show all chapter solutions

Ch. 7.1 - Given a function f from a set X to a set Y, f(x)...Ch. 7.1 - Given a function f from a set X to a set Y, if...Ch. 7.1 - Given a sunction f from a set X to a set Y, the...Ch. 7.1 - Given a function f then a set X to a set Y, if...Ch. 7.1 - Given a function f from a set X to a set Y, if yY...Ch. 7.1 - Given functions f and g from a set X to a set Y....Ch. 7.1 - Given positive real numbers x and b with b1 ....Ch. 7.1 - Given a function f from a set X to a set Y and a...Ch. 7.1 - Given a function f from a set X to a set Y and a...Ch. 7.1 - Let X={l,3,5} and Y=a,b,c,d) . Define g:XY by the...

Ch. 7.1 - Let X={1,3,5} and Y={a,b,c,d}. Define g:XY by the...Ch. 7.1 - Indicate whether the statement in parts (a)-(d)...Ch. 7.1 - a. Find all function from X={a,b}toY={u,v} . b....Ch. 7.1 - Let Iz be the identity function defined on the set...Ch. 7.1 - Find function defined on the sdet of nonnegative...Ch. 7.1 - Let A={1,2,3,4,5} , and define a function F:P(A)Z...Ch. 7.1 - Let Js={0,1,2,3,4} , and define a function F:JsJs...Ch. 7.1 - Define a function S:Z+Z+ as follows: For each...Ch. 7.1 - Let D be the set of all finite subsets of positive...Ch. 7.1 - Define F:ZZZZ as follows: For every ordered pair...Ch. 7.1 - Let JS={0,1,2,3,4} ,and define G:JsJsJsJs as...Ch. 7.1 - Let Js={0,1,2,3,4} , and define functions f:JsJs...Ch. 7.1 - Define functions H and K from R to R by the...Ch. 7.1 - Let F and G be functions from the set of all real...Ch. 7.1 - Let F and G be functions from the set of all real...Ch. 7.1 - Use the definition of logarthum to fill in the...Ch. 7.1 - Find exact values for each of the following...Ch. 7.1 - Use the definition of logarithm to prove that for...Ch. 7.1 - Use the definition of logarithm to prove that for...Ch. 7.1 - If b is any positive real number with b1 and x is...Ch. 7.1 - Use the unique factorizations for the integers...Ch. 7.1 - If b and y are positive real numbers such that...Ch. 7.1 - If b and y are positivereal numbers such that...Ch. 7.1 - Let A={2,3,5} and B={x,y}. Let p1 and p2 be the...Ch. 7.1 - Observe that mod and div can be defined as...Ch. 7.1 - Let S be the set of all strings of as and bs....Ch. 7.1 - Consider the coding and decoding functions E and D...Ch. 7.1 - Consider the Hamming distance function defined in...Ch. 7.1 - Draw arrow diagram for the Boolean functions...Ch. 7.1 - Fill in the following table to show the values of...Ch. 7.1 - Cosider the three-place Boolean function f defined...Ch. 7.1 - Student A tries to define a function g:QZ by the...Ch. 7.1 - Student C tries to define a function h:QQ by the...Ch. 7.1 - Let U={1,2,3,4} . Student A tries to define a...Ch. 7.1 - Let V={1,2,3} . Student C tries to define a...Ch. 7.1 - On certain computers the integer data type goed...Ch. 7.1 - Let X={a,b,c} and Y={r,s,tu,v,w} , Define f:XY as...Ch. 7.1 - Let X={1,2,3,4} and Y={a,b,c,e} . Define g:XY as...Ch. 7.1 - Let X and Y be sets, let A and B be any subsets of...Ch. 7.1 - In 41-49 let X and Y be sets, let A and B be any...Ch. 7.1 - In 41-49 let X and Y be sets, let A and B be any...Ch. 7.1 - In 41-49 let X and Y be sets, let A and B be any...Ch. 7.1 - In 41-49 let X and Y be sets, let A and B be any...Ch. 7.1 - In 41-49 let X and Y be sets, let A and B be any...Ch. 7.1 - In 41-49 let X and Y be sets, let A and B be any...Ch. 7.1 - In 41-49 let X and Y be sets, let A and B be any...Ch. 7.1 - In 41-49 let X and Y be sets, let A and B be any...Ch. 7.1 - In 41-49 let X and Y be sets, let A and B be any...Ch. 7.1 - Given a set S and a subset A, the characteristic...Ch. 7.1 - Each of exercises 51-53 refers to the Euler phi...Ch. 7.1 - Each of exercises 51-53 refers to the Euler phi...Ch. 7.1 - Each of exercises 51-53 refers to the Euler phi...Ch. 7.2 - If F is a function from a set X to a set Y, then F...Ch. 7.2 - If F is a function from a set X to a set Y, then F...Ch. 7.2 - If F is a function from a set X to a set Y, then F...Ch. 7.2 - If F is a function from a set X to a set Y, then F...Ch. 7.2 - The following two statements are_______....Ch. 7.2 - Given a function F:XY where X is an infinite set,...Ch. 7.2 - Given a function F:XY where X is an infinite set,...Ch. 7.2 - Given a function F:XY , to prove that F is not one...Ch. 7.2 - Given a function F:XY , to prove that F is not...Ch. 7.2 - A one-to-one correspondence from a set X to a set...Ch. 7.2 - If F is a one-to-one correspondence from a set X...Ch. 7.2 - The definition of onr-to-one is stated in two...Ch. 7.2 - Fill in each blank with the word most or least. a....Ch. 7.2 - When asked to state the definition of one-to-one,...Ch. 7.2 - Let f:XY be a function. True or false? A...Ch. 7.2 - All but two of the following statements are...Ch. 7.2 - Let X={1,5,9} and Y={3,4,7} . a. Define f:XY by...Ch. 7.2 - Let X={a,b,c,d} and Y={e,f,g} . Define functions F...Ch. 7.2 - Let X={a,b,c} and Y={d,e,f,g} . Define functions H...Ch. 7.2 - Let X={1,2,3},Y={1,2,3,4} , and Z= {1,2} Define a...Ch. 7.2 - a. Define f:ZZ by the rule f(n)=2n, for every...Ch. 7.2 - Define F:ZZZZ as follows. For every ordered pair...Ch. 7.2 - a. Define F:ZZ by the rule F(n)=23n for each...Ch. 7.2 - a. Define H:RR by the rule H(x)=x2 , for each real...Ch. 7.2 - Explain the mistake in the following “proof.”...Ch. 7.2 - In each of 15-18 a function f is defined on a set...Ch. 7.2 - In each of 15-18 a function f is defined on a set...Ch. 7.2 - In each of 15-18 a function f is defined on a set...Ch. 7.2 - In each of 15-18 a function f is defined on a set...Ch. 7.2 - Referring to Example 7.2.3, assume that records...Ch. 7.2 - Define Floor: RZ by the formula Floor (x)=x , for...Ch. 7.2 - Let S be the set of all string of 0’s and 1’s, and...Ch. 7.2 - Let S be the set of all strings of 0’s and 1’s,...Ch. 7.2 - Define F:P({a,b,c})Z as follaws: For every A in...Ch. 7.2 - Les S be the set of all strings of a’s and b’s,...Ch. 7.2 - Let S be the et of all strings is a’s and b’s, and...Ch. 7.2 - Define S:Z+Z+ by the rule: For each integer n,...Ch. 7.2 - Let D be the set of all set of all finite subsets...Ch. 7.2 - Define G:RRRR as follows:...Ch. 7.2 - Define H:RRRR as follows: H(x,y)=(x+1,2y) for...Ch. 7.2 - Define J=QQR by the rule J(r,s)=r+2s for each...Ch. 7.2 - De?ne F:Z+Z+Z+ and G:Z+Z+Z+ as follows: For each...Ch. 7.2 - a. Is log827=log23? Why or why not? b. Is...Ch. 7.2 - The properties of logarithm established in 33-35...Ch. 7.2 - The properties of logarithm established in 33-35...Ch. 7.2 - The properties of logarithm established in 33-35...Ch. 7.2 - Exercise 36 and 37 use the following definition:...Ch. 7.2 - Exercise 36 and 37 use the following definition:...Ch. 7.2 - Exercises 38 and 39 use the following definition:...Ch. 7.2 - Exercises 38 and 39 use the following definition:...Ch. 7.2 - Suppose F:XY is one—to—one. a. Prove that for...Ch. 7.2 - Suppose F:XY is into. Prove that for every subset...Ch. 7.2 - Let X={a,b,c,d,e}and Y={s,tu,v,w}. In each of 42...Ch. 7.2 - Let X={a,b,c,d,e}and Y={s,tu,v,w}. In each of 42...Ch. 7.2 - In 44-55 indicate which of the function in the...Ch. 7.2 - In 44-55 indicate which of the function in the...Ch. 7.2 - In 44-55 indicate which of the function in the...Ch. 7.2 - In 44-55 indicate which of the function in the...Ch. 7.2 - In 44-55 indicate which of the function in the...Ch. 7.2 - In 44-55 indicate which of the function in the...Ch. 7.2 - In 44-55 indicate which of the function in the...Ch. 7.2 - In 44-55 indicate which of the function in the...Ch. 7.2 - In 44-55 indicate which of the functions in the...Ch. 7.2 - In 44-55 indicate which of the functions in the...Ch. 7.2 - In 44-55 indicate which of the functions in the...Ch. 7.2 - In 44-55 indicate which of the functions in the...Ch. 7.2 - In Example 7.2.8 a one-to-one correspondence was...Ch. 7.2 - Write a computer algorithm to check whether a...Ch. 7.2 - Write a computer algorithm to check whether a...Ch. 7.3 - If f is a function from X to Y’,g is a function...Ch. 7.3 - If f is a function from X to Y and Ix and Iy are...Ch. 7.3 - If f is a one-to=-one correspondence from X to Y....Ch. 7.3 - If f is a one-to-one function from X to Y and g is...Ch. 7.3 - If f is an onto function from X to Y and g is an...Ch. 7.3 - In each of 1 and 2, functions f and g are defined...Ch. 7.3 - In each of 1 and 2, functions f and g are defined...Ch. 7.3 - In 3 and 4, functions F and G are defined by...Ch. 7.3 - In 3 and 4, functions F and G are defined by...Ch. 7.3 - Define f:RR by the rule f(x)=x for every real...Ch. 7.3 - Define F:ZZ and G:ZZ . By the rules F(a)=7a and...Ch. 7.3 - Define L:ZZ and M:ZZ by the rules L(a)=a2 and...Ch. 7.3 - Let S be the set of all strings in a’s and b’s and...Ch. 7.3 - Define F:RR and G:RZ by the following formulas:...Ch. 7.3 - Define F:ZZ and G:ZZ by the rules F(n)=2n and...Ch. 7.3 - Define F:RR and G:RR by the rules F(n)=3x and...Ch. 7.3 - The functions of each pair in 12—14 are inverse to...Ch. 7.3 - G:R+R+ and G1:RR+ are defined by G(x)=x2andG1(x)=x...Ch. 7.3 - H and H-1 are both defined from R={1} to R-{1} by...Ch. 7.3 - Explain how it follows from the definition of...Ch. 7.3 - Prove Theorem 7.3.1(b): If f is any function from...Ch. 7.3 - Prove Theorem 7.3.2(b): If f:XY is a one-to-one...Ch. 7.3 - Suppose Y and Z are sets and g:YZ is a one-to-one...Ch. 7.3 - If + f:XY and g:YZ are functions and gf is...Ch. 7.3 - If f:XY and g:YZ are function and gf is onto, must...Ch. 7.3 - If f:XY and g:YZ are function and gf is...Ch. 7.3 - If f:XY and g:YZ are functions and gf is onto,...Ch. 7.3 - Let f:WZ,g:XY , and h:YZ be functions. Must...Ch. 7.3 - True or False? Given any set X and given any...Ch. 7.3 - True or False? Given any set X and given any...Ch. 7.3 - In 26 and 27 find (gf)1,g1,f1, and f1g1 , and...Ch. 7.3 - In 26 and 27 find (gf)1,g1,f1 , and f1g1 by the...Ch. 7.3 - Prove or given a counterexample: If f:XY and g:YX...Ch. 7.3 - Suppose f:XY and g:YZ are both one-to-one and...Ch. 7.3 - Let f:XY and g:YZ. Is the following property true...Ch. 7.4 - A set is finite if, and only if,________Ch. 7.4 - To prove that a set A has the same cardinality as...Ch. 7.4 - The reflexive property of cardinality says that...Ch. 7.4 - The symmetric property of cardinality says that...Ch. 7.4 - The transitive property of cardinality say that...Ch. 7.4 - A set called countably infinite if, and only...Ch. 7.4 - A set is called countable if, and only if,_______Ch. 7.4 - In each of the following, fill in the blank the...Ch. 7.4 - The cantor diagonalization process is used to...Ch. 7.4 - When asked what it means to say that set A has the...Ch. 7.4 - Show that “there are as many squares as there are...Ch. 7.4 - Let 3Z={nZn=3k,forsomeintegerk} . Prove that Z and...Ch. 7.4 - Let O be the set of all odd integers. Prove that O...Ch. 7.4 - Let 25Z be the set of all integers that are...Ch. 7.4 - Use the functions I and J defined in the paragraph...Ch. 7.4 - (a) Check that the formula for F given at the end...Ch. 7.4 - Use the result of exercise 3 to prove that 3Z is...Ch. 7.4 - Show that the set of all nonnegative integers is...Ch. 7.4 - In 10-14 s denotes the sets of real numbers...Ch. 7.4 - In 10-14 s denotes the sets of real numbers...Ch. 7.4 - In 10-14 S denotes the set of real numbers...Ch. 7.4 - In 10—14 S denotes the set of real numbers...Ch. 7.4 - In 10—14 S denotes the set of real numbers...Ch. 7.4 - Show that the set of all bit string (string of 0’s...Ch. 7.4 - Show that Q, that set of all rational numbers, is...Ch. 7.4 - Show that Q, the set of all rational numbers, is...Ch. 7.4 - Must the average of two irrational numbers always...Ch. 7.4 - Show that the set of all irrational numbers is...Ch. 7.4 - Give two examples of functions from Z to Z that...Ch. 7.4 - Give two examples of function from Z to Z that are...Ch. 7.4 - Define a function g:Z+Z+Z+ by the formula...Ch. 7.4 - âa. Explain how to use the following diagram to...Ch. 7.4 - Prove that the function H defined analytically in...Ch. 7.4 - Prove that 0.1999….=0.2Ch. 7.4 - Prove that any infinite set contain a countable...Ch. 7.4 - Prove that if A is any countably infinite set, B...Ch. 7.4 - Prove that a disjoint union of any finite set and...Ch. 7.4 - Prove that a union of any two countably infinite...Ch. 7.4 - Use the result of exercise 29 to prove that the...Ch. 7.4 - Use the results of exercise 28 and 29 to prove...Ch. 7.4 - Prove that ZZ , the Cartesian product of the set...Ch. 7.4 - Use the results of exercises 27, 31, and 32 to...Ch. 7.4 - Let P(s) be the set of all subsets of set S, and...Ch. 7.4 - Let S be a set and P(S) be the set of all subsets...Ch. 7.4 - `The Schroeder-Bernstein theorem states the...Ch. 7.4 - Prove that if A and B are any countably infinite...Ch. 7.4 - Suppose A1,A2,A3,.... is an infinite sequence of...

Find more solutions based on key concepts

Show solutions APPLICATIONS
Average cost A company’s average cost per unit when x units are produced is defined to be
Use t...

Mathematical Applications for the Management, Life, and Social Sciences

AGE DISTRIBUTION OF RENTERS A study conducted by the Metro Housing Agency in a Midwestern city revealed the fol...

Finite Mathematics for the Managerial, Life, and Social Sciences

Show that the graph is 2-colorable by finding a 2-coloring. If the graph is not 2-colorable, explain why.

Mathematical Excursions (MindTap Course List)

Read the measurement shown on each U.S. micrometer:

Elementary Technical Mathematics

Express 3.5% as a common fraction.

Mathematics For Machine Technology

Exercises 22-27 involve the information in Figure 9.116 on constructing a home. Create the Gantt chart for cons...

Mathematics: A Practical Odyssey

Identifying a Conic In Exercises 23-26, use a graphing utility to graph the polar equation. Identify the graph ...

Calculus (MindTap Course List)

Consider the type of clothes dryer (gas or electric) purchased by each of five different customers at a certain...

Probability and Statistics for Engineering and the Sciences

Using Horizontal Asymptotes In Exercises 37-40, match the function with its graph. Use horizontal asymptotes as...

Calculus: An Applied Approach (MindTap Course List)

Sketch the vector field F by drawing a diagram like Figure 5 or Figure 9. 7. F(x, y, z) = i

Multivariable Calculus

Entertainment Spend. The Wall Street Journal asked Concur Technologies, Inc., an expense-management company, to...

Essentials Of Statistics For Business & Economics

Let x denote the amount of gravel sold (in tons) during a randomly selected week at a particular sales facility...

Introduction To Statistics And Data Analysis

Use a graph to find a number N such that if x N then |3x2+12x2+x+11.5|0.05

Calculus: Early Transcendentals

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

Applied Calculus

In what direction u is Du f(−1, 1) maximum for f(x, y) = x3y4?
⟨3, −4⟩
⟨4, −3⟩

Study Guide for Stewart's Multivariable Calculus, 8th

Use Newtons method with initial approximation x1 = 1 to find x2, the second approximation to the root of the eq...

Single Variable Calculus: Early Transcendentals

Solve the following word problems. Round dollars to the nearest cent and percents to the nearest tenth of a per...

Contemporary Mathematics for Business & Consumers

Determining Convergence or Divergence In Exercises 29-44, determine the convergence or divergence of the sequen...

Calculus: Early Transcendental Functions (MindTap Course List)

Simplify the expressions in Exercises 97106. 21/a/22/a

Finite Mathematics and Applied Calculus (MindTap Course List)

Domain of a Composition Find the functions f g and g f and their domains. 85. f(x) = 2x, g(x) = x + 1

Precalculus: Mathematics for Calculus (Standalone Book)

Evaluating an Iterated Integral In Exercises 11-28, evaluate the iterated integral. 023y26y2yy23ydxdy

Multivariable Calculus

12. Find all normal subgroups of the quaternion group.

Elements Of Modern Algebra

π
does not exist

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

The volume of a right circular cone is V=13r2h, where r is the radius of the base and h is the height. (a) Find...

Single Variable Calculus

Annual salary plus bonus data for chief executive officers are presented in the business-Week Annual Pay Survey...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A researcher conducts an independent-measures, two- factor study with two levels of factor A and two levels of ...

Statistics for The Behavioral Sciences (MindTap Course List)

In each of the following problems, the binomial distribution will be used. Answers may vary slightly depending ...

Understanding Basic Statistics

Does the regression equation from Problem 20 account for a significant portion of the variance in the Y scores?...

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

Given point D in the interior of RST, suppose that RG=3,GS=4,SH=4,HT=5, and TK=3. Find KR.

Elementary Geometry For College Students, 7e

Critical Numbers Use a graphing utility to graph the following four functions. Only one of the functions has cr...

Calculus: Early Transcendental Functions

Describe the four methods for administering a survey (mail, phone, Internet, and in person) and explain the str...

Research Methods for the Behavioral Sciences (MindTap Course List)

Write each angle as a sum or difference involving 2. For example, 5/3=2/3. 116

Trigonometry (MindTap Course List)

let f(x) = x 1, g(x) = x+1, and h(x) = 2x3 1. Find the rule for each function. 17. f-hg

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

Proof Let f and g be one-to-one functions. Prove that (a) fg is one-to-one. (b) (fg)1(x)=(g1f1)(x)

Calculus of a Single Variable

Reminder Round all answers to two decimal places unless otherwise indicated. Ponzi Schemes A Ponzi scheme is a ...

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

Identify and describe the steps of the scientific method.

Research Methods for the Behavioral Sciences (MindTap Course List)

In a distribution of scores with a mean of 35 and a standard deviation of 4, which event is more likely: that a...

Essentials Of Statistics

Use synthetic division to perform each division. 4x43x3x+5x3

College Algebra (MindTap Course List)

17-36 Differentiate the function. y=(lntanx)2

Calculus (MindTap Course List)

When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we will ra...

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

Find the height of the regular square pyramid shown if each edge of the base measures 8 in. and the length of t...

Elementary Geometry for College Students

If f is differentiable at a, where a 0, evaluate the following limit in terms of f'(a): limxaf(x)f(a)xa

Single Variable Calculus: Early Transcendentals, Volume I

For Problems 51-66, use an algebraic approach to solve each problem. Objective 2 An apartment complex contains ...

Intermediate Algebra

For the following exercises, evaluate the functions. Give the exact value. 210. sin1(1)

Calculus Volume 1

The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modificat...

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

In the following Exercises, find each indefinite integral, using appropriate substitutions. 399. dx9+x2

Calculus Volume 2

Identifying a Conic In Exercises 83-90, identify the conic by writing its equation in standard form. Then sketc...

College Algebra

70. A new automated production process averages 1.5 breakdowns per day. Because of the cost associated with a b...

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