   # Fill in the blanks in the following proof that for all sets A and B, ( A − B ) ∩ ( B − A ) = ∅ . Proof: Let A and B be any sets and suppose ( A − B ) ∩ ( B − A ) ≠ ∅ . That is, suppose there is an element x in (a) . By definition of (b) x ε A − B and x ε A − B and x ε . (c) Then by definition of set difference, x ε A and x ∉ B and x ∈ (d) and x ∉ (e) In particular x ∈ A and x ∉ (f) which is a contradiction. Hence [the supposition that ( A − B ) ∩ ( B − A ) ≠ ∅ is false, and so] (g) ### 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 27ES
Textbook Problem
1 views

## Fill in the blanks in the following proof that for all sets A and B, ( A − B ) ∩ ( B − A ) = ∅ . Proof: Let A and B be any sets and suppose ( A − B ) ∩ ( B − A ) ≠ ∅ . That is, suppose there is an element x in (a) . By definition of (b) x   ε   A − B and x   ε   A − B and x   ε   . (c) Then by definition of set difference, x   ε A and x   ∉ B and x   ∈ (d) and x   ∉ (e) In particular x   ∈ A and x   ∉ (f) which is a contradiction. Hence [the supposition that ( A − B )   ∩ ( B − A ) ≠ ∅ is false, and so] (g)

To determine

To Prove:

For all subsets Aof a universal set U,AAc=.

### Explanation of Solution

Given information:

Let  A  be any set

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

Let A be any subset of the universal set.

The objective is to prove the result AAc= for all subsets A of universal set.

Use the contradiction method to prove the result.

Suppose that AAc=.

Let xAAc

By the definition of intersection, xAand xAc

### 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 problems 37-42, solve each equation using a graphing utility.

Mathematical Applications for the Management, Life, and Social Sciences

Focal Length A refracting telescope has a main lens, or objective lens, and a second lens, the eyepiece see Fig...

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

In Exercises 2330, factor each expression and simplify as much as possible. (x2+1)x+1(x+1)3

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the integral. 58. xlnxx21dx

Single Variable Calculus

The length of the are r = e for 0 is given by: a) 0ed b) 02e2d c) 02ed d) 02ed

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

let f(x) = x3 + 5, g(x) = x2 2, and h(x)= 2x + 4. Find the rule for each function. 3. fg

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

Finding Derivatives In Exercises 51-62, find f(x). f(x)=6x3+3x22x+1x

Calculus: An Applied Approach (MindTap Course List) 