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 , B , and C , if A ⊆ B then A ∩ C ⊆ B ∩ C .

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 16ES
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,B, and C, if

A ⊆ B then A ∩ C ⊆ B ∩ C .

To determine

To prove:

For all sets A,B and C, if A⊆B and A⊆C then A⊆B∩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 if A⊆B and A⊆C then A⊆B∩C

To show A⊆B∩C, it is enough to show that ∀x, if x∈A then x∈B∩C.

Let x∈A and A⊆B, A⊆C

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution
arrow_back
Chapter 6.2,
Problem 15ES
Chapter 6.2,
Problem 17ES
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
Find the unknown area, length, or width for each of the rectangles 31 through 42. Where necessary, round the an...

Mathematics For Machine Technology

Use the table below, which shows the number of students at a university who are currently in each class level. ...

Mathematical Excursions (MindTap Course List)

Solve the equations in Exercises 126. x4x2=6

Finite Mathematics

Find each product mentally: (x9)(x8)

Elementary Technical Mathematics

In problems 5-8, Use a calculator to evaluate the indicated powers. 8.

Mathematical Applications for the Management, Life, and Social Sciences

In Exercises 21-30, find the indicated products if they exist of the matrices given in Exercises 1-10. a. AB b....

Mathematics: A Practical Odyssey

In Exercises 1-18, construct a truth table for each compound proposition. (pq)(p~q)

Finite Mathematics for the Managerial, Life, and Social Sciences

Consider the following data for a dependent variable y and two independent variables, x1 and x2. Develop an es...

Essentials Of Statistics For Business & Economics

Find the limit. limx0sin5x3x

Single Variable Calculus: Early Transcendentals, Volume I

Engine Displacement The displacement for an automobile engine is the total volume displaced by the cylinders in...

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

Convert the expressions in Exercises 8596 radical form. y7/4

Applied Calculus

Finding an Equation of a Tangent Plane and a Normal Line In Exercises 17-26,(a) find an equation of the tangent...

Calculus: Early Transcendental Functions (MindTap Course List)

The revenue and cost equations for a product are R=x600.0001xandC=12x+1,800,000 where R and C are measured in d...

College Algebra

Find if is between 0 and 90. Round your answers to the nearest tenth of a degree. cos=0.9770

Trigonometry (MindTap Course List)

The value of property for tax purposes is known as the ___ value. The value of property based on location, size...

Contemporary Mathematics for Business & Consumers

Find integer bounds for the zeros of each function. Answers can vary. P(x)=x5+x48x38x2+15x+15

College Algebra (MindTap Course List)

8. 2 and age 4 compared to children who drank whole or 2% milk (Scharf, Demmer, and DeBoer, 2013). Is this an e...

Statistics for The Behavioral Sciences (MindTap Course List)

Finding Derivatives In Exercises 1-24, find the derivative of the function. See Examples 1, 2, 4, 5, and 8. f(t...

Calculus: An Applied Approach (MindTap Course List)

When the length of each edge of a cube is increased by 1 cm, the volume is increase by 61 cm3. What is the leng...

Elementary Geometry For College Students, 7e

Calculate y'. 4. y=tanx1+cosx

Calculus: Early Transcendentals

Many older homes have electrical systems that use fuses rather than circuit breakers. A manufacturer of 40-amp ...

Probability and Statistics for Engineering and the Sciences

(a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylors Inequality to estimate ...

Single Variable Calculus

If 1 kg equals 2.2 lb, use a proportion to convert 12 pounds to kilograms.

Elementary Geometry for College Students

Small Business: Bankruptcy The National Council of Small Businesses is interested in the proportion of small bu...

Understanding Basic Statistics

Using the power series for cos x, the sum of the series is: cos(0.0625) cos(0.25) cos(0.5)

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

Evaluating a Logarithm Using Technology In Exercises 5-8, use a graphing utility to evaluate the logarithm by (...

Calculus of a Single Variable

A sample of 16 items provides a sample standard deviation of 9.5. Test the following hypotheses using = .05. W...

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

In Exercises 2340, find the indicated limit. 30. limx0(4x520x2+2x+1)

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

Using PsycINFO (or a similar database), find five articles on the topic of preschool daycare and social anxiety...

Research Methods for the Behavioral Sciences (MindTap Course List)

Find a parametric representation for the surface. 25. The part of the cylinderx2+ y2+ z2 =36 that lies between ...

Multivariable Calculus

Duck hunting in populated areas faces opposition on the basis of safety and environmental issues. In asurvey to...

Introduction To Statistics And Data Analysis

Research has demonstrated strong gender differences in teenagers approaches to dealing with mental health issue...

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

Inequalities Involving Quotients Solve the nonlinear inequality. Express the solution using interval notation, ...

Precalculus: Mathematics for Calculus (Standalone Book)

Suppose (hat a complex therapy procedure contains one component that has absolutely no effect on behavior. Expl...

Research Methods for the Behavioral Sciences (MindTap Course List)

Which is true about the series ? diverges converges absolutely converges conditionally converges, but not absol...

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 3148, (a) factor the given expression, and (b) set the expression equal to zero and solve for the ...

Finite Mathematics and Applied Calculus (MindTap Course List)

Finding a Particular Solution In Exercises 37-44, find the particular solution of the differential equation tha...

Calculus (MindTap Course List)

Finding When using the definition of limit to prove that L. is the limit of f (x) as x approaches c, you find ...

Calculus: Early Transcendental Functions

SOC The table that follows reports the marital status of 20 respondents in two different apartment complexes. H...

Essentials Of Statistics

The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has...

Calculus (MindTap Course List)

For Problems 5-54, perform the following operations with real numbers. Objectives 3-6 1112(534)

Intermediate Algebra

Label each of the following statements as either true or false. The field of rational numbers is complete.

Elements Of Modern Algebra

Finding the Curl of a Vector Field Using Technology In Exercise 49 and 50, use a computer algebra system to fin...

Multivariable Calculus

The DATAfile EngineeringSalary contains the median starting salary and median midcareer salary (measured 10 yea...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

AreaIn Exercises 29 and 30, use a double integral to find the area of the shaded region.

Calculus

Evaluate the integral. 9. 23dx(x21)3/2

Single Variable Calculus: Early Transcendentals

bartleby
© bartleby 2020