   # Let the universal set be R, the set of all real number, and let A = { x ∈ R|0&lt;x ≤ 2 } B = { x ∈ R | 1 ≤ x &lt; 4 } , and C = { x ∈ R | 3 ≤ x &lt; 9 } . Find each of the following: a. A ∪ B b. A ∩ B c. A e d. A ∪ C e. A ∩ C f. B e g. A e ∩ B e h. A c ∪ B x i. ( A ∩ B ) x j. ( A ∪ B ) x ### 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 11ES
Textbook Problem
1 views

## Let the universal set be R, the set of all real number, and let A = { x ∈ R|0<x ≤ 2 } B = { x ∈ R | 1 ≤ x < 4 } , and C = { x ∈ R | 3 ≤ x < 9 } .Find each of the following:a. A ∪ B b. A ∩ B c. A e d. A ∪ C e. A ∩ C f. B e g. A e ∩ B e h. A c ∪ B x i. ( A ∩ B ) x j. ( A ∪ B ) x

To determine

(a)

Find the value of

AB

### Explanation of Solution

Given information:

Three sets A,B and C are defined as follows.

A={xR|0<x,2},B={xR|1x<4}, and C={xR|3x<9}

Where, R is the universal set of real numbers.

Concept used:

Three sets A,B and C are defined as follows.

A={xR|0<x,2},B={xR|1x<4}, and C={xR|3x<9}

Where, R is the universal set of real numbers.

These sets on real number lines are as shown below.

Calculation:

Consider the set.

AB

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

From the definitionof of set union

To determine

(b)

Find the value of

AB

To determine

(c)

Find the value of

Ac

To determine

(d)

Find the value of

AC

To determine

(e)

Find the value of

AC

To determine

(f)

Find the value of

Bc

To determine

(g)

Find the value of

AcBc

To determine

(h)

Find the value of

AcBc

To determine

(i)

Find the value of

(AB)c

To determine

(j)

Find the value of

(AB)c

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