   # Use an element argument to prove each statement in 7-22. Assume that all sets are subsets of a universal set U . For all set A, B , and C , ( A − B ) ∩ ( C − B ) = ( A ∩ C ) − 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 13ES
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 set A, B, and C, ( A − B ) ∩ ( C − B ) = ( A ∩ C ) − B .

To determine

To prove:

For all sets A,B and C, if AB then ACBC.

### Explanation of Solution

Given information:

Let A,B and C are sets.

Concept used:

:Union of sets:Intersection of sets

Calculation:

Let A,B and C are sets.

Prove that, if AB then ACBC.

According to the definition of subset, the statement AB means that for every element in A is in the set B.

Suppose x is any element in AC, by definition of intersection xA and xC

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