   # 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 , ( A ∪ B ) − C ⊆ ( A − C ) ∪ ( 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 12ES
Textbook Problem
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## 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, ( A ∪ B ) − C ⊆ ( A − C ) ∪ ( B − C ) .

To determine

To prove:

For all sets A,Aϕ=A.

### Explanation of Solution

Given information:

Let A be any sets.

Concept used:

:Union of sets:Intersection of sets

Calculation:

For A=A, it is enough to prove that A=A and AA.

Show AA as follows.

Suppose xA.

A={x:xA or x}={x:xA}=A

By the definition of union, xA because is empty set

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