   # Let S i = { x ∈ R|1&lt;x&lt;1+ 1 i } = ( 1 , 1 + 1 i ) for each positive integer i . ∪ i = 0 4 S i = ? ∩ i = 0 4 S i = ? Are S 1 , S 2 , S 3 , ... mutually disjoint? Explain. ∪ i = 0 n S i = ? ∩ i = 0 x S i = ? ∪ i = 0 ∞ S i = ? ∩ i = 0 ∞ S i = ? ### 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 6.1, Problem 26ES
Textbook Problem
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## Let S i = { x ∈ R|1<x<1+ 1 i } = ( 1 , 1 + 1 i ) for each positive integer i. ∪ i = 0 4 S i = ? ∩ i = 0 4 S i = ? Are S 1 , S 2 , S 3 , ...   mutually disjoint? Explain. ∪ i = 0 n S i = ? ∩ i = 0 x S i = ? ∪ i = 0 ∞ S i = ? ∩ i = 0 ∞ S i = ?

To determine

(a)

Calculate the value of i=04Si.

### Explanation of Solution

Given information:

Let Si={xR|1<x<1+1i}=(1,1+1i) for each positive integer i.

Calculation:

Si={xR|1<x<1+1i}=(1,1+1i)

Let us first determine S1,S2,S3 and S4.

S1={xR|1<x<1+11}={xR|1<x<2}=(1,2)

S2={xR|1<x<1+12}={xR|1<x<32}=(1,32)

S3={xR|1<x<1+13}={

To determine

(b)

Calculate the value of i=04Si.

To determine

(c)

Whether S1,S2,S3,.... mutually disjoint or not.

To determine

(d)

Calculate the value of i=0nSi.

To determine

(e)

Calculate the value of i=0nSi.

To determine

(f)

Calculate the value i=0Si.

To determine

(g)

Calculate the value of i=0Si.

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