   # 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 B ∩ C ⊆ A , t h e n ( C − A ) ∩ ( B − A ) = ∅ ### 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 37ES
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 B ∩ C ⊆ A ,   t h e n   ( C − A ) ∩ ( B − A ) = ∅

To determine

To Prove:

If BCA then (CA)(BA)=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 show that if BCA then (CA)(BA)=.

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

Suppose (CA)(BA)=.

Then there is an element x(CA)(BA).

By definition of intersection xCA and xBA

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