   # 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 ⊆ C and B ⊆ C then A ∪ 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 20ES
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 ⊆ C and B ⊆ C then A ∪ B ⊆ C .

To determine

To prove:

Find the mistake in the following “proof” that for all sets A,B and C, if AB and BC then AC.

Suppose A,B and C are sets such that AB and BC. Since AB, there is an element x such that xA and xB. Since BC, there is an element x such that xA and xC. Hence there is an element x such that xA and xC and so AC.

### 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 are any sets.

Prove that. If AB and BC then AC.

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

But the proof given in me text book, dealt with a single element x in the set A.

So the statement “Since AB, there exists an element x such that xA and xB is false.

Also the statement ‘since BC, there exists an element x such that xB and xC is false,

The other error in the proof ¡s occurs in the last step

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