   # Use an element argument to prove each statement in 7—22. Assume that all sets are subsets of a universal set ∪ . 11. For all sets A , B , and C , A ∩ ( B − C ) ⊆ ( A ∩ B ) − ( A ∩ 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 11ES
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 ∪ . 11. For all sets A, B, and C, A ∩ ( B − C ) ⊆ ( A ∩ B ) − ( A ∩ C ) .

To determine

To prove:

For all sets A and B,A(AB)=A.

### Explanation of Solution

Given information:

A and B Be two sets.

Concept used:

:Union of sets:Intersection of sets

Calculation:

Let A and B be any sets.

The objective is to prove that A(AB)=A for all sets A and B.

To show A(AB)=A, it is enough to show that A(AB)A and AA(AB).

Show that A(AB)A.

That is x, if xA(AB) then xA.

Let xA(AB).

By the definition of union xA or xAB

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