   # Use the element method for proving a set equals the empty set to prove each statement in 28—38. Assume that all sets are subsets of a universal set ∪ . 28. For all sets A and B , ( A ∩ B ) ∩ ( A ∩ B c ) = ∅ . (This property is used in Section 9.9.) ### 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 28ES
Textbook Problem
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## Use the element method for proving a set equals the empty set to prove each statement in 28—38. Assume that all sets are subsets of a universal set ∪ .28. For all sets A and B, ( A ∩ B ) ∩ ( A ∩ B c ) = ∅ . (This property is used in Section 9.9.)

To determine

To Prove:

If U denotes a universal set, then Uc=ϕ.

### Explanation of Solution

Given information:

Consider that a universal set U.

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

Consider that a universal set U.

The objective is to find Uc=ϕ by using the element method for proving a set equal to empty set.

Element method for proving a set equal to empty set:

To prove that a set X is equal to the empty set ϕ, prove that X has no element. To do this,

Suppose X has an element and derive a contradiction.

Prove that the set Uc={x|xis not in U}=ϕ by using the element method as,

Since all sets are subsets of the universal set U

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