   # Let B i = { x ∈ R|0 ≤ x ≤ i } for each integer i = 1 , 2 , 3 , 4. a. B 1 ∪ B 2 ∪ B 3 ∪ B 4 = ? b. B 1 ∩ B 2 ∩ B 3 ∩ B 4 = ? c. Are B 1 , B 2 , B 3 , and B 4 mutually disjoint? Explain. ### 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 20ES
Textbook Problem
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## Let B i = { x ∈ R|0 ≤ x ≤ i } for each integer i = 1 , 2 , 3 , 4. a. B 1 ∪ B 2 ∪ B 3 ∪ B 4 = ? b. B 1 ∩ B 2 ∩ B 3 ∩ B 4 = ? c. Are B 1 , B 2 , B 3 , and B 4 mutually disjoint? Explain.

To determine

(a)

B1B2B3B4

### Explanation of Solution

Given information:

Bi={xR|0xi}, for all integers i=1,2,3, and 4.

Concept used:

B1={xR|0x1}=[0,1]B2={xR|0x2}=[0,2]B3={xR|0x3}=[0,3]B4={xR|0x4}=[0,4]

Calculation:

Consider the set,

B1B2B3B4

The objective is to determine the set B1B2B3B4 from the above defined sets.

From the definition of set union,

AB={xU|xA or xB}

To determine

(b)

B1B2B3B4

To determine

(c)

Are B1,B2,B3andB4 mutually disjoin? Explain.

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