Intermediate Algebra (11th edition)

108 CHAPTER 2 Linear Equations, Inequalities, and Applications

Applying Intersection and Union

The five highest-grossing domestic films (adjusted for inflation) as of 2009 are listed

in the table.

EXAMPLE 9

Five All-Time Highest-Grossing Domestic Films

NOW TRY
EXERCISE 9
In Example 9,list the
elements that satisfy each set.

(a)The set of films with
admissions greater than
140,000,000 and gross
income less than
$1,200,000,000

(b)The set of films with
admissions less than
200,000,000 or gross
income less than
$1,200,000,000

Film Admissions Gross Income

Gone with the Wind 202,044,600 $1,450,680,400

Star Wars 178,119,600 $1,278,898,700

The Sound of Music 142,415,400 $1,022,542,400

E.T. 141,854,300 $1,018,514,100

The Ten Commandments 131,000,000 $ 940,580,000

Source:boxofficemojo.com.

List the elements of the following sets.

(a)The set of the top five films with admissions greater than 180,000,000 andgross

income greater than $1,000,000,000

The only film that satisfies both conditions is Gone with the Wind,so the set is

(b)The set of the top five films with admissions less than 140,000,000 orgross

income greater than $1,000,000,000

Here, any film that satisfies at least one of the conditions is in the set. This set

includes all five films:

NOW TRY

5 Gone with the Wind, Star Wars, The Sound of Music, E.T., The Ten Commandments 6.

5 Gone with the Wind 6.

NOW TRY ANSWERS

9. (a){The Sound of Music, E.T.}
   (b){Star Wars, The Sound of
   Music, E.T., The Ten
   Commandments}

Complete solution available
on the Video Resources on DVD

2.6 EXERCISES

Concept Check Decide whether each statement is trueor false. If it is false, explain why.

1.The union of the solution sets of , , and is.

2.The intersection of the sets and is.

3.The union of the sets and is.

4.The intersection of the sets and is.

5.The intersection of the set of rational numbers and the set of irrational numbers is.

6.The union of the set of rational numbers and the set of irrational numbers is the set of real

numbers.

Let ,,and. Specify each set.

See Examples 1 and 5.

7. 
   
   
   
   8. 
      
      
      
      9. 
         
         
         
         10. 11.B ̈ 0 12.A ̈ 0 13.A ́B 14.B ́D
         
         
         
         
      
      
      
      
   
   
   
   

B ̈A A ̈B A ̈D B ̈C

A= 5 1, 2, 3, 4, 5, 6 6 B= 5 1, 3, 5 6 C= 5 1, 6 6 D= 546

506

1 - q, 7 4 3 7, q 2 576

1 - q, 7 2 1 7, q 2 576

5 x |xÚ 96 5 x |x... 96 0

x+ 1 = 6 x+ 166 x+ 176 1 - q, q 2