   # Use an element argument to prove each statement in 28-38. Assume that all sets are subsets of a universal set U. For every set 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 32ES
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 every set A , A × ∅ = ∅ .

To determine

To Prove:

For all sets A, A×ϕ=ϕ.

### Explanation of Solution

Given information:

The objective is to find use element method to find for all sets A, A×ϕ=ϕ.

Concept used:

:Union of sets:Intersection of sets

: subset of set

: Null set

Calculation:

Definition: (element method to proving a set equal the empty set)

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

Suppose X has an element and derive contradiction.

Prove that the set A×ϕ=ϕ is empty as,

That is, it is enough to show that the set A×ϕ has no elements

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