   # Use an element argument to prove each statement in 7-22. Assume that all sets are subsets of universal set U . For every set A , A ∪ ∅ = 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 15ES
Textbook Problem
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## Use an element argument to prove each statement in 7-22. Assume that all sets are subsets of universal set U.For every set A , A ∪ ∅ = A .

To determine

To prove:

For all sets A and B, if AB then BcAc.

### Explanation of Solution

Given information:

Let A and B are two sets.

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

The objective is to prove that if AB then BcAc for all sets A and B.

To prove that the set BcAc it is enough to show that each element xBc then xAc.

For that,

Let xBc then by the definition of complement xUBxB.

Claim: the element xAc.

The definition of subset the statement AB means every element in A is in the set B

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