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 = ?

Q: Expert Answer

To determine (a) Calculate the value of ∪ i = 0 4 S i . Explanation Given information: Let S i = { x ∈ R | 1 < x < 1 + 1 i } = ( 1 , 1 + 1 i ) for each positive integer i. Calculation: S i = { x ∈ R | 1 < x < 1 + 1 i } = ( 1 , 1 + 1 i ) Let us first determine S 1 , S 2 , S 3 and S 4 . S 1 = { x ∈ R | 1 < x < 1 + 1 1 } = { x ∈ R | 1 < x < 2 } = ( 1 , 2 ) S 2 = { x ∈ R | 1 < x < 1 + 1 2 } = { x ∈ R | 1 < x < 3 2 } = ( 1 , 3 2 ) S 3 = { x ∈ R | 1 < x < 1 + 1 3 } = { To determine (b) Calculate the value of ∩ i = 0 4 S i . To determine (c) Whether S 1 , S 2 , S 3 , .... mutually disjoint or not. To determine (d) Calculate the value of ∪ i = 0 n S i . To determine (e) Calculate the value of ∩ i = 0 n S i . To determine (f) Calculate the value ∪ i = 0 ∞ S i . To determine (g) Calculate the value of ∩ i = 0 ∞ S i .

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Answer 1

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Answer 2

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Discrete Mathematics With Applicat...

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Solutions

Chapter

Section

Answer 3

Solutions

Chapter

Section

Answer 4

Chapter

Section

Answer 5

To determine

(a)

Calculate the value of ∪i=04Si.

Explanation of Solution

Given information:

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

Calculation:

Si={x∈R|1<x<1+1i}=(1,1+1i)

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

S1={x∈R|1<x<1+11}={x∈R|1<x<2}=(1,2)

S2={x∈R|1<x<1+12}={x∈R|1<x<32}=(1,32)

S3={x∈R|1<x<1+13}={

Answer 6

To determine

(b)

Calculate the value of ∩i=04Si.

Answer 7

To determine

(c)

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

Answer 8

To determine

(d)

Calculate the value of ∪i=0nSi.

Answer 9

To determine

(e)

Calculate the value of ∩i=0nSi.

Answer 10

To determine

(f)

Calculate the value ∪i=0∞Si.

Answer 11

To determine

(g)

Calculate the value of ∩i=0∞Si.

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 = ?

Discrete Mathematics With Applicat...

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Discrete Mathematics With Applicat...