   # Use the element method for proving a set equals the empty set to prove each statement in 28-38. Assume that all sets are subsets of a universal set U. For all sets A , B , and C , ( A − C ) ∩ ( B − C ) ∩ ( A − B ) = ∅ . ### 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 29ES
Textbook Problem
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## Use the element method for proving a set equals the empty set to prove each statement in 28-38. Assume that all sets are subsets of a universal set U. For all sets A, B, and C, ( A − C ) ∩ ( B − C ) ∩ ( A − B ) = ∅ .

To determine

To prove:

For all sets A,BandC, (AC)(BC)(AB)=.

### Explanation of Solution

Given:

Three random sets A,BandC.

Concept used:

If an element xAB, then xAandxB.

If an element xAB, then xAandxB.

Proof:

Assume that (AC)(BC)(AB)

Then there exists an element x(AC)(BC)(AB)

xACandxBCandxAB     (By the definition of intersection)

(xAandxC)and(xBandxC)and(xAand

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