   # 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 , ( A ∩ B ) e = A e ∪ B c . ### Discrete Mathematics With Applicat...

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

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193
Chapter 6.2, Problem 7ES
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, ( A ∩ B ) e = A e ∪ B c .

To determine

To prove:

For all sets A and B, (AB)c=AcBc

### Explanation of Solution

Given information:

A and B be two sets.

Concept used:

:Union of sets:Intersection of sets

Calculation:

Let A and B be any sets.

The objective is to prove that (AB)c=AcBc for all sets A and B.

To show (AB)c=AcBc, it is enough to show that (AB)cAcBc and AcBc(AB)c Show that (AB)cAcBc.

That is x, if x(AB)c, then x(AB)c.

Let x(AB)c

By the definition of complement, xAB

By the definition of intersection, either xA and xB

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
In Exercises 15-22, use the laws of logarithms to solve the equation. logx(116)=2

Finite Mathematics for the Managerial, Life, and Social Sciences

Simplify: j6

Elementary Technical Mathematics

[Type here] In Problems 11-14, find the inverses of matrix and check it by calculating. 14. [Type here]

Mathematical Applications for the Management, Life, and Social Sciences

What is a geodesic?

Mathematical Excursions (MindTap Course List)

29. Let . Prove that if and then .

Elements Of Modern Algebra

In Exercises 14, find the values of x that satisfy the inequality (inequalities). 4. 2x2 50

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

Find an equation of the slant asymptote. Do not sketch the curve. y=4x310x211x+1x23x

Single Variable Calculus: Early Transcendentals, Volume I

True or False: If f′(c) = 0 and f″(c) < 0, then c is a local minimum.

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

True or False: converges conditionally.

Study Guide for Stewart's Multivariable Calculus, 8th

Prove: If ab=cd where b0 and d0, then a+bb=c+dd.

Elementary Geometry For College Students, 7e

In Exercises 7-10, solve the equation. 3x210x+8=0

Calculus: An Applied Approach (MindTap Course List)

Reminder Round all answers to two decimal places unless otherwise indicated. Competition Between Bacteria Suppo...

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