   # Let R i = { x ∈ R|1 ≤ x ≤ 1 + 1 i } = [ 1 , 1 + 1 i ] for each positive integer i . ∪ i = 0 4 R i = ? ∩ i = 0 4 R i = ? Are R 1 , R 2 , R 3 , ... mutually disjoint? Explain. ∪ i = 0 n R i = ? ∩ i = 0 n R i = ? ∪ i = 0 ∞ R i = ? ∩ i = 0 ∞ R 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 25ES
Textbook Problem
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## Let R i = { x ∈ R|1 ≤ x ≤ 1 + 1 i } = [ 1 , 1 + 1 i ]   for   each positive integer  i . ∪ i = 0 4 R i = ? ∩ i = 0 4 R i = ? Are R 1 , R 2 , R 3 , ... mutually disjoint? Explain. ∪ i = 0 n R i = ? ∩ i = 0 n R i = ? ∪ i = 0 ∞ R i = ? ∩ i = 0 ∞ R i = ?

To determine

(a)

Calculate i=04Ri.

### Explanation of Solution

Given information:

Let Ri={xR|1x1+1i}=[1,1+1i] for each positive integer i.

Calculation:

Ri={xR|1x1+1i}=[1,1+1i]

Let us first determine R1,R2,R3 and R4

R1={xR|1x1+11}={xR|1x2}=[1,2]R2={xR|1x1+12}={xR|1x32}=[1,32]R3={xR|1x1+13}={</

To determine

(b)

Calculate i=04Ri.

To determine

(c)

Determine whether R1,R2,R3,.... mutually disjoint or not.

To determine

(d)

Calculate i=0nRi.

To determine

(e)

Calculate i=0nRi.

To determine

(f)

Calculate i=0Ri.

To determine

(g)

Calculate i=0Ri.

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