   # Let V i = { x ∈ R | − 1 i ≤ x ≤ 1 i } = [ − 1 i , 1 i ] for each positive integer i . a. ∪ i = 0 4 V i = ? b. ∩ i = 0 4 V i = ? c. Are mutually disjoint V 1 V 2 V 3 , ... mutually disjoint? Explain. d. ∪ i = 0 n V i = ? e. ∩ i = 0 n V i = ? f. ∪ i = 0 ∞ V i = ? g. ∩ i = 0 ∞ V 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 23ES
Textbook Problem
1 views

## Let V i = { x ∈ R | − 1 i ≤ x ≤ 1 i } = [ − 1 i , 1 i ] for each positive integer i.a. ∪ i = 0 4 V i = ? b. ∩ i = 0 4 V i = ? c. Are mutually disjoint V 1 V 2 V 3 , ... mutually disjoint? Explain.d. ∪ i = 0 n V i = ? e. ∩ i = 0 n V i = ? f. ∪ i = 0 ∞ V i = ? g. ∩ i = 0 ∞ V i = ?

To determine

(a)

Calculate i=04Vi.

### Explanation of Solution

Given information:

Let Vi={xR|1ix1i}=[1i,1i] for each positive integer i.

Calculation:

Vi={xR|1ix1i}=[1i,1i]

Let us first determine V1,V2,V3 and V4.

V1={xR|11x11}={xR|1x1}V2={xR|12x12}V3={xR|13x<

To determine

(b)

Calculate i=04Vi.

To determine

(c)

Find out whether V1,V2,V3,.... mutually disjoint or not.

To determine

(d)

Calculate i=0nVi.

To determine

(e)

Calculate i=0nVi.

To determine

(f)

Calculate i=0Vi.

To determine

(g)

Calculate i=0Vi.

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