   # Use an element argument 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 , if C ⊆ B − A , then A ∩ 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 36ES
Textbook Problem
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## Use an element argument 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, if C ⊆ B − A , then A ∩ C = ∅ .

To determine

To Prove:

For all sets A,B and C if CBAthen AC=ϕ

### Explanation of Solution

Given information:

Let A,B and C be any sets.

Concept used:

:Union of sets:Intersection of sets

: subset of set

: Null set

Calculation:

The objective is to prove the result AC= is true for ail A,B and C such that CBA.

Use the contradiction method to prove the result.

Let A,B and C be any sets such that CBA.

Suppose that AC.

Let xAC

By tile definition of intersection xA and xC

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