   Chapter 6.3, Problem 24ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Let A = { t , u , v , w } , and let S 1 be the set of all subsets of A that do not contain w and S 2 the set of all subsets of A that contain w. Find S 1 . Find S 2 Are S 1 and S 2 . Compare the sizes of S 1 and S 2 . How many elements are S 1 ∪ S 2 ? What is the relation between S 1 ∪ S 2 and P ( A ) ?

To determine

Let S={a,b,c} and let Sa be the set of all subsets of S that contain a, let Sb be the set of all subsets of S that contain b, let Sc be the set of all subsets of S that contain c, and let Sϕ be the set whose only element is ϕ is {Sa,Sb,Sc,Sϕ} a partition of (S) ?.

Explanation

Given information Let S={a,b,c} and let Sa be the set of all subsets of S that contain a, let Sb be the set of all subsets of S that contain b, let Sc be the set of all subsets of S that contain c.

Concept used:

Sa= set of all subsets of S={a,b,c} containing a

Calculation:

Sa= set of all subsets of S={a,b,c} containing a ={{a},{a,b},{a,c},{a,b,c}}.

Sb= set of all subsets of S containing b

={{b},{a,b},{b,c},{a,b,c}}

Sc= set of all subsets of S containing c

={{c},{a,c},{b,c},{a,b,c}}

Sϕ={ϕ}

{Sa,Sb,Sc,Sϕ} is not a partition of P(S), while SaSbSc={{a,b,c}}

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