menu
bartleby
search
close search
Hit Return to see all results
Subscribe
Sign in
Math
Discrete Mathematics With Applications5th Edition
close solutoin list

Use an element argument to prove each statement in 7-22. Assume that all sets are subsets of a universal set U . For all sets A and B , if A ⊆ B then B e ⊆ A e

BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

Solutions

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

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193
Chapter 6.2, Problem 18ES
Textbook Problem
1 views

Use an element argument to prove each statement in 7-22. Assume that all sets are subsets of a universal set U.

For all sets A and B, if A ⊆ B then B e ⊆ A e

To determine

To prove:

A×(B∪C)=(A×B)∪(A×C)

Explanation of Solution

Given information:

Let A,B and C be any sets.

Concept used:

∪:Union of sets∩:Intersection of sets

⊆: subset of set

Calculation:

Let A,B and C be any sets.

The objective is to prove that A×(B∪C)=(A×B)∪(A×C) for all sets A,B and C.

To show A×(B∪C)=(A×B)∪(A×C). It is enough to prove A×(B∪C)⊆(A×B)∪(A×C) and (A×B)∪(A×C)⊆A×(B∪C).

Show that A×(B∪C)⊆(A×B)∪(A×C).

That is ∀x, if x∈A×(B∪C), then x∈(A×B)∪(A×C).

Let x=(a,b)∈A×(B∪C).

By the definition of cross product a∈A and b∈B∪C.

By the definition of union, a∈A and [b∈B or b∈C].

This implies that [a∈A and b∈B] or [a∈A and b∈C].

By the definition of cross product, [(a,b)∈A×B] or [(a,b)∈A×C].

By the definition of union, (a,b)∈(A×B)∪(A×C).

Thus, fo all (a,b)∈A×(B∪C) then (a,b)∈(A×B)∪(A×C)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution
arrow_back
Chapter 6.2,
Problem 17ES
Chapter 6.2,
Problem 19ES
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 6 Solutions

Discrete Mathematics With Applications
Show all chapter solutions
add
Ch. 6.1 - The notation is read”______” and means that___Ch. 6.1 - To use an element argument for proving that a set...Ch. 6.1 - To disprove that a set X is a subset of set Y, you...Ch. 6.1 - An element x is in AB if , and only if,_______Ch. 6.1 - An element x in AB if, and only if,______Ch. 6.1 - An element x is in B-A if, and only if,______Ch. 6.1 - An elements x is in Acif, and only if.______Ch. 6.1 - The empty set is a set with ______Ch. 6.1 - The power set of a set A is _____Ch. 6.1 - Sets A and B are disjoint if, and only...
Ch. 6.1 - A collection of nonempty set is a partition of a...Ch. 6.1 - In each of (a)-(f), answer the following question:...Ch. 6.1 - Complete the proof from Example 6.1.3: Prove that...Ch. 6.1 - Let sets R, S, and T be defined as follows:...Ch. 6.1 - Let A={nZn=5rforsomeintegerr} and...Ch. 6.1 - Let C={nZn=6r5forsomeintegerr} and...Ch. 6.1 - Let...Ch. 6.1 - ...Ch. 6.1 - Write in words how to end to read each of the...Ch. 6.1 - Complete the following sentences without using the...Ch. 6.1 - ...Ch. 6.1 - Let the universal set be R, the set of all real...Ch. 6.1 - Let the universal set be R, the set of all real...Ch. 6.1 - Let S be the set of all strings of 0’s and 1’s of...Ch. 6.1 - In each of the following, draw a Venn diagram for...Ch. 6.1 - In each of the following, draw a Venn diagram for...Ch. 6.1 - Let A={a,b,c},B={b,c,d} , and C={b,c,e} a. Find...Ch. 6.1 - Consider the following Venn diagram. For each of...Ch. 6.1 - a. Is the number 0 in ? Why? b. Is ={} ? Why ? c....Ch. 6.1 - Let Ai={i,i2} for each integer i=1,2,3,4. a....Ch. 6.1 - Let Bi={xR0xi} for each integer i=1,2,3,4. a....Ch. 6.1 - Let Ci={i,i} for each nonnegative integer i.Ch. 6.1 - Let Di={xR-ixi}=[i,i] for each nonnegative integer...Ch. 6.1 - Let Vi={xR1ix1i}=[1i,1i] for each positive integer...Ch. 6.1 - Let Wi={xRxi}=(i,) for each nonnegative integer i....Ch. 6.1 - Let Ri={xR1x1+1i}=[1,1+1i]foreachpositiveintegeri....Ch. 6.1 - Let Si={xR1x1+1i}=(1,1+1i) for each positive...Ch. 6.1 - a. Is {{a, d, e}, {b, c}, {d, f }} a partition of...Ch. 6.1 - Let E be the set of all even integers and O the...Ch. 6.1 - Let R be the set of all real number. Is a...Ch. 6.1 - Let Z be the set of all integers and let...Ch. 6.1 - Suppose A={1,2} and B={2,3} . Find each of the...Ch. 6.1 - Suppose A={1} and B={u,v} . Find P(AB) . Suppose...Ch. 6.1 - Find P() FindP(p()). Find p(p(p())) .Ch. 6.1 - Let A1={1},A2={u,v},andA3={m,n}. Find each of the...Ch. 6.1 - Let...Ch. 6.1 - Trace the action of Algorithm 6,1,1 on the...Ch. 6.1 - Trace the action of Algorithm 6,1,1 on the...Ch. 6.1 - Write an algorithm to determine whether a given...Ch. 6.2 - To prove that a set X is a subset of a set you...Ch. 6.2 - To prove that a set X is a subset of a set AB, you...Ch. 6.2 - To prove that a set ABis a subset of a set X, you...Ch. 6.2 - To prove that a set AB is a subset of a set X, you...Ch. 6.2 - To prove that a set X equals a set Y, you prove...Ch. 6.2 - To prove that a set X does not equal a set Y, you...Ch. 6.2 - To say that an element is in A(BC) means that it...Ch. 6.2 - The following are two proofs that for all sets A...Ch. 6.2 - In 3 and 4, supply explanations of the steps in...Ch. 6.2 - Theorem: For all sets A and B, if AB , then ABB.Ch. 6.2 - Prove that for all set A and B, (BA)=BAe .Ch. 6.2 - Let and stand for the words “intersection” and...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an elements argument to prove each statement...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Find the mistake in the following : proof” that...Ch. 6.2 - Find the mistake in all the following “proof.”...Ch. 6.2 - Find the mistake in the following “proof” that for...Ch. 6.2 - Consider the Venn diagram below. Illustrate one of...Ch. 6.2 - Fill in the blanks in the following proof that for...Ch. 6.2 - Use the element method for proving a set equals...Ch. 6.2 - Use the element method for proving a set equals...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Use an element argument to prove each statement in...Ch. 6.2 - Prove each statement is 39-44. For all sets A and...Ch. 6.2 - Prove each statement in 39-44. For every positive...Ch. 6.2 - Prove each statement in 39-44. For every positive...Ch. 6.2 - Prove each statement in 39-44. For every positive...Ch. 6.2 - Prove each statement in 39-44. For every positive...Ch. 6.2 - Prove each statement in 39-44. For every positive...Ch. 6.3 - Given a proposed set identity set identity...Ch. 6.3 - When using algebraic method for proving a set...Ch. 6.3 - When applying a property from Theorem 6.2.2, it...Ch. 6.3 - For each of 1-4 find a counterexample to show that...Ch. 6.3 - For each of 1-4 find a counterexample to show that...Ch. 6.3 - For each of 1-4 find a counterexample to show that...Ch. 6.3 - For each of 1-4 find a counterexample to show that...Ch. 6.3 - For each of 5—21 prove each statement that is true...Ch. 6.3 - For each of 5-21 prove each statement that is true...Ch. 6.3 - For each of 5-21 prove each statement that is true...Ch. 6.3 - For each of 5-21 prove each statement that is true...Ch. 6.3 - For each of 5-21 prove each statement that is true...Ch. 6.3 - For each of 5-21 prove each statement that is true...Ch. 6.3 - For each of 5-21 prove each statement that I true...Ch. 6.3 - For each of 5-21 prove each statement that I true...Ch. 6.3 - For each of 5—21 prove each statement that is true...Ch. 6.3 - For each of 5-21 prove each statement that I true...Ch. 6.3 - For each of 5-21 prove each statement that I true...Ch. 6.3 - For each of 5-21 prove each statement that I true...Ch. 6.3 - For each of 5-21 prove each statement that is true...Ch. 6.3 - For each of 5-21 prove each statement that is true...Ch. 6.3 - For each of 5-21 prove each statement that I true...Ch. 6.3 - For each of 5-21 prove each statement that is true...Ch. 6.3 - For each of 5-21 prove each statement that is true...Ch. 6.3 - Write a negation for each of the following...Ch. 6.3 - Let S={a,b,c} and for each integer i = 0, 1, 2, 3,...Ch. 6.3 - Let A={t,u,v,w} , and let S1 be the set of all...Ch. 6.3 - Use mathematical induction to prove that for every...Ch. 6.3 - The following problem, devised by Ginger Bolton,...Ch. 6.3 - In 27 and 28 supply a reason fro each step in the...Ch. 6.3 - In 27 and 28 supply a reason fro each step in the...Ch. 6.3 - Some steps are missing from the following proof...Ch. 6.3 - In 30-40, construct an algebraic proof for the...Ch. 6.3 - In 30-40, construct an algebraic proof for the...Ch. 6.3 - In 30-40, construct an algebraic proof for the...Ch. 6.3 - In 30-40, construct an algebraic proof for the...Ch. 6.3 - In 30-40, construct an algebraic proof for the...Ch. 6.3 - In 30—40, construct an algebraic proof for the...Ch. 6.3 - In 30-40, construct an algebraic proof for the...Ch. 6.3 - In 30-40, construct an algebraic proof for the...Ch. 6.3 - In 30-40, construct an algebraic proof for the...Ch. 6.3 - In 30-40, construct an algebraic proof for the...Ch. 6.3 - In 30-40, construct an algebraic proof for the...Ch. 6.3 - In 41-13 simple the given expression. Cite a...Ch. 6.3 - In 41-43 simplify the given expression. Cite a...Ch. 6.3 - In 41-43 simlify the given expression. Cite a...Ch. 6.3 - Consider the following set property: For all sets...Ch. 6.3 - Consider the following set property: For all sets...Ch. 6.3 - Let A={1,2,3,4},B={3,4,5,6}, and C={5,6,7,8} Find...Ch. 6.3 - Refer to the definition of symmetric difference...Ch. 6.3 - Refer to the definition of symmetric difference...Ch. 6.3 - Refer to the definition of symmetric difference...Ch. 6.3 - Refer to the definition of symmetric difference...Ch. 6.3 - Refer to the definition of symmetric difference...Ch. 6.3 - Refer to the definition of symmetric difference...Ch. 6.3 - Derive the set identity A(AB)=A from the...Ch. 6.3 - Derive the set identity A(AB)=A from the...Ch. 6.4 - In the comparison between the structure of the set...Ch. 6.4 - The operations of + and in a Boolean algebra are...Ch. 6.4 - Russell showed that the following proposed “set...Ch. 6.4 - In 1-3 assume that B is a Boolean algebra with...Ch. 6.4 - In 1-3 assume that B is a Boolean algebra with...Ch. 6.4 - In 1-3 assume that B is a Boolean algebra with...Ch. 6.4 - In 4—10 assume that B is a Boolean algebra with...Ch. 6.4 - In 4—10 assume that B is a Boolean algebra with...Ch. 6.4 - In 4—10 assume that B is a Boolean algebra with...Ch. 6.4 - In 4—10 assume that B is a Boolean algebra with...Ch. 6.4 - In 4—10 assume that B is a Boolean algebra with...Ch. 6.4 - In 4—10 assume that B is a Boolean algebra with...Ch. 6.4 - In 4—10 assume that B is a Boolean algebra with...Ch. 6.4 - Let S = {O, 1}, and define operations + and · on S...Ch. 6.4 - Exercises 12-15 provide an outline for a proof...Ch. 6.4 - Exercises 12-15 provide an outline for a proof...Ch. 6.4 - Exercises 12-15 provide an outline for a proof...Ch. 6.4 - Exercises 12-15 provide an outline for a proof...Ch. 6.4 - In 16-21 determine wheter each sentence is a...Ch. 6.4 - In 16-21 determine wheter each sentence is a...Ch. 6.4 - In 16-21 determine where each sentence is a...Ch. 6.4 - In 16-21 determin whether each sentence is a...Ch. 6.4 - In 16-21 determine wherether each sentence is a...Ch. 6.4 - In 16-21 determine wherether each sentence is a...Ch. 6.4 - (a) Assuming that the following senetec is a...Ch. 6.4 - The following two sentences were devised by the...Ch. 6.4 - Can there exist a cimputer program that has as...Ch. 6.4 - Can there exist a book that refers to all those...Ch. 6.4 - Some English adjectives are descriptive of...Ch. 6.4 - As strange as it may seem, it is possible to give...Ch. 6.4 - Is there an alogroithm whichm for a fixed quantity...Ch. 6.4 - Use a technique similar to that used to derive...

Additional Math Textbook Solutions

Find more solutions based on key concepts
Show solutions add
Complete the table: Architects estimate Maximum rate above estimate Maximum acceptable bid 8,275,625 5

Elementary Technical Mathematics

11. If $2500 is deposited at the end of each quarter in an account that earns compounded quarterly, after how ...

Mathematical Applications for the Management, Life, and Social Sciences

What is the Alabama Paradox? Explain its meaning.

Mathematics: A Practical Odyssey

For each of the following functions of angles, write the cofunction of the complement of the angle. sin36

Mathematics For Machine Technology

IDENTITY FRAUD The identity fraud rates in the United States for the years 2005-2011 are given in the following...

Finite Mathematics for the Managerial, Life, and Social Sciences

Convert the expressions in Exercises 6584 to power form. 3x1.2213x2.1

Finite Mathematics

Find each quotient and remainder in the same base as the given numerals. 457twelve5twelve

Mathematical Excursions (MindTap Course List)

For Problems 47-54, translate each English phrase into an algebraic expression, and use n to represent the unkn...

Intermediate Algebra

For the following second mortgage applications, calculate the percentage of appraised value and the potential c...

Contemporary Mathematics for Business & Consumers

Using Newton's Method In Exercises 7-18, use Newton's Method to approximate the zero(s) of the function. Contin...

Calculus: Early Transcendental Functions (MindTap Course List)

Evaluate 4sin(2x+2) when x is 6.

Trigonometry (MindTap Course List)

The article cited in Exercise 20 also gave the following values of the variables y = number of culs-de-sac and ...

Probability and Statistics for Engineering and the Sciences

(a) We define the improper integral (over the entire plane 2) I=R2e(x2+y2)dA=e(x2+y2)dydx=limaDae(x2+y2)dA wher...

Multivariable Calculus

Prove: In a parallelogram, the sum of the squares of the lengths of its diagonals is equal to the sum of the sq...

Elementary Geometry for College Students

For the limit limx2(x33x+4)=6 illustrate Definition 2 by finding values of that correspond =0.2 and 0.1. Def...

Single Variable Calculus: Early Transcendentals, Volume I

A psychologist determined that the number of sessions required to obtain the trust ofa new patient is either 1,...

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

ReminderRound all answers to two decimal places unless otherwise indicated. Cancer Mortality RatesThe graph in ...

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

Label each of the following statements as either true or false. 3. Let , , and be mappings from into such th...

Elements Of Modern Algebra

The solution to y″ − 10y′ + 25y = 0, y(0) = 5, y(1) = 0 is: y = 5e5x − xe5x y = 5e5x − 5xe5x y = e5x − 5xe5x y ...

Study Guide for Stewart's Multivariable Calculus, 8th

The following data show the number of rental cars in service for three rental car companies: Hertz, Avis, and D...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A normal distribution has a mean of =54 and a standard deviation of =6 . What is the probability of randomly se...

Statistics for The Behavioral Sciences (MindTap Course List)

Interpretation You are applying for two jobs, and you estimate the probability of getting an offer for the firs...

Understanding Basic Statistics

Find f(x). Check that your answer is reasonable by comparing the graphs of f and f. 62. f(x) = arctan(x2 x)

Single Variable Calculus: Early Transcendentals

The 2000 Census showed that the town of Grandville had a population of 1020 residents. The 2010 Census was 1170...

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

Evaluating Basic Limits In Exercises 13-20, find the limit. See Example 3. limx1x3

Calculus: An Applied Approach (MindTap Course List)

A jogger runs along two sides of an open rectangular lot. If the first side of the lot is 200 ft long and the d...

Elementary Geometry For College Students, 7e

Fill in the blanks. An equation of the form ax+b=0 is called a ______ equation.

College Algebra (MindTap Course List)

Converting a Rectangular EquationIn Exercises 7986, convert the rectangular equation to an equation in (a) cyli...

Calculus

Determine whether the series is convergent or divergent. 12. n=1n2+1n3+1

Calculus: Early Transcendentals

Given are five observations collected in a regression study on two variables. Develop a scatter diagram for th...

Essentials Of Statistics For Business & Economics

Using Different Methods In Exercises 71 and 72, (a) sketch the graph of the polar equation, (b) determine the i...

Calculus (MindTap Course List)

Differentiate. 34. y=ecosx+cos(ex)

Single Variable Calculus

Equations of Circles Find an equation of the circle that satisfies the given conditions. 94. Endpoints of a dia...

Precalculus: Mathematics for Calculus (Standalone Book)

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Applied Calculus

Volume Consider the region bounded by the graphs of y=x16x2,y=0,x=0,andx=4. Find the volume of the solid genera...

Calculus of a Single Variable

Exercises You can use the following problems as a self-test on the material presented in this review. If you ca...

Essentials Of Statistics

Alternative Formula for the Principal Unit Normal Vector In Exercises 53-56, use the vector-valued function r(t...

Multivariable Calculus

The following matrix represents the results (the means) from a 2 2 factorial study. One mean is not given. Al ...

Research Methods for the Behavioral Sciences (MindTap Course List)

In Exercises 35-42, find functions f and g such that h = g f. (Note: The answer is not unique.) 39. h(x)=1x21

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

Use PsycINFO or a similar database to find a quasi-experimental or non-experimental research study. (Note: Try ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Expand each expression in Exercises 122. (y1y)(y+1y)

Finite Mathematics and Applied Calculus (MindTap Course List)

Sum of a Finite Arithmetic Sequence In Exercises 45-50, find the sum of the finite arithmetic sequence. 5+3+1+1...

College Algebra

Identifying Graphs In Exercises 149 and 150, the graphs of a function f and its derivative f ' are shown. Label...

Calculus: Early Transcendental Functions

Find the domain of the function. f(x)=2x35x2+x6

Calculus (MindTap Course List)

The authors of the paper Digital Inequality: Differences in Young Adults Use of the Internet (Communication Res...

Introduction To Statistics And Data Analysis

A sample with a mean of M = 8 has X = 56. How many scores are in the sample?

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

bartleby
© bartleby 2020