   Chapter 6.3, Problem 23ES ### 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 S = { a , b , c } and for each integer i = 0, 1, 2, 3, let S i be the set of all subsets of S that have I elements. List the elements in S 0 , S 1 , S 2 , and S 3 .Is { S 0 , S 1 , S 2 ,   S 3 } a partition of P ( S ) ?

To determine

Let S=(a,b,c) and for each integer i=0,1,2,3, let Si be the set of all subsets of S that have i elements. List the elements in S0,S1,S2 andS3 is {S0,S1,S2,S3} a partition of (S) ?

Explanation

Given information Let S=(a,b,c) and for each integer i=0,1,2,3, let Si be the set of all subsets of S that have i elements

Concept used:

P(s):Power of sets

Calculation:

Consider S0 as follows:

S0 Be the set of all subsets of S that have 0 element.

So, S0=ϕ

Consider S1 as follows:

S1 Be the set of all subsets of S that have 1 element.

S1 Has one element set ={{a},{b},{c}}

Consider S2 as follows:

S2 Be the set of all subsets of S that have 2 elements.

S2 Has two element sets ={{a,b},{a,c},{b,c}}

Consider S3 as follows:

S3 Be the set of all subsets of S that have 3 elements.

S3 Has three element sets ={a,b,c}

A finite or infinite collection of nonempty sets {A1,A2,...........,An,....} is called a partition of a set A if the following conditions hold:

A is the union of all Ai.

The sets A1,A2,...........,An,

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