   # 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 ⊆ B then A ∩ C ⊆ 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 16ES
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 ⊆ B then A ∩ C ⊆ B ∩ C .

To determine

To prove:

For all sets A,B and C, if AB and AC then ABC.

### 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 any sets.

The objective is to prove that if AB and AC then ABC

To show ABC, it is enough to show that x, if xA then xBC.

Let xA and AB, AC

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