   # Use an element argument to prove each statement in 7-22. Assume that all sets are subsets of a universal set U . For all sets A , B , and C , if A ⊆ B then A ∪ C ⊆ B ∪ 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 17ES
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 sets A , B , and C , if A ⊆ B then A ∪ C ⊆ B ∪ C .

To determine

To prove:

For all sets A,B and C, if AC and BC then ABC.

### Explanation of Solution

Given information:

Let A,B and C be any sets.

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

Let A,B and C be any sets.

The objective is to prove that is AC and BC then ABC.

To show ABC, it is enough to prove that x, if xAB,then xC.

Let show xAB and AB and AC.

By the definition of union xA or xB

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