   # Consider the Venn diagram below. Illustrate one of the distributive laws by shading in the region corresponding to A ∪ ( B ∩ C ) on one copy of the diagram and ( A ∪ B ) ∩ ( A ∪ C ) on another. Illustrate the other distributive law by shading in the region corresponding to A ∪ ( B ∩ C ) on one copy of the diagram and ( A ∪ B ) ∩ ( A ∪ C ) on another. Illustrate one of De Morgan's laws by shading In the region corresponding to ( A ∪ B ) c on one copy of the diagram and A c ∩ B c on the other. (Leave the set C out of your diagrams.) Illustrate the other De Morgan's law by shad- ing in the region corresponding to on A c ∩ B c one copy of the diagram and A c ∩ B c on the other. (Leave the set C out of your diagrams.) ### 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 26ES
Textbook Problem
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## Consider the Venn diagram below. Illustrate one of the distributive laws by shading in the region corresponding to   A ∪ ( B ∩ C ) on one copy of the diagram and   ( A ∪ B ) ∩ ( A ∪ C ) on another. Illustrate the other distributive law by shading in the region corresponding to A ∪ ( B ∩ C ) on one copy of the diagram and   ( A ∪ B ) ∩ ( A ∪ C ) on another. Illustrate one of De Morgan's laws by shading In the region corresponding to ( A ∪ B ) c on one copy of the diagram and A c ∩ B c on the other. (Leave the set C out of your diagrams.) Illustrate the other De Morgan's law by shad- ing in the region corresponding to on A c ∩ B c one copy of the diagram and A c ∩ B c on the other. (Leave the set C out of your diagrams.)

To determine

To Prove:

For all sets A,B,and C,

(AC)(BC)(AB)=ϕ

### Explanation of Solution

Given information:

Let  A , B and C be any set

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

The objective is to prove that (AC)(BC)(AB)=ϕ, for all sets A,B,and C.

Consider,

(AC)(BC)(AB)={x|xACand xBCand xAB }={x|xACcand xBCcand xABc}By set difference law.={x|(xAand xC)and(xBand xC)and (xAandxB)}

={x|xAand (xB<

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