   # 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 A ⊆ B and B ∩ C = ∅ 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 35ES
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 A ⊆ B and B ∩ C = ∅ then A ∩ C = ∅ .

To determine

To Prove:

For all sets A,B and C if AB and BC=ϕ then 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:

Let A,B and C be three sets.

Prove that if AB and BC=ϕ then AC=ϕ.

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

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