Beginning Algebra, 11th Edition

9.The set of positive even integers

10.The set of all multiples of 5

11.Which of the sets described in Exercises 1–10are infinite sets?

12.Which of the sets described in Exercises 1–10are finite sets?

Concept Check Tell whether each statement is trueor false.

Let

and

Tell whether each statement is trueor false.See Examples 3, 5, 6, and 7.

31.There are exactly 4 subsets of E. 32.There are exactly 8 subsets of D.

33.There are exactly 12 subsets of C. 34.There are exactly 16 subsets of B.

Let

and

List the elements in each set. See Examples 4 –7.

61.Name every pair of disjoint sets among sets A–Din the directions for Exercises 45 – 60.

62.Show that for sets Band Din the directions for Exercises 45 – 60,

1 B ́D 2 ¿=B¿ ̈D¿.

C ́B C ́D A ̈ 0 B ́ 0

B ̈C A ́B B ́D B ́C

A ̈B B ̈A A ̈D B ̈D

A¿ B¿ C¿ D¿

B= 5 a, c, e 6 , C= 5 a, f 6 , D= 5 d 6.

U= 5 a, b, c, d, e, f, g, h 6 , A= 5 a, b, c, d, e, f 6 ,

5 5, 10, 15, 20 6 ́ 5 5, 15, 30 6 = 5 5, 15 6

5 4, 9, 11, 7, 3 6 ́ 5 1, 2, 3, 4, 5 6 = 5 1, 2, 3, 4, 5, 7, 9, 11 6

5 3, 5, 7, 9 6 ́ 5 4, 6, 8 6 = 0 5 1, 2, 3 6 ́ 5 1, 2, 3 6 = 5 1, 2, 3 6

5 3, 9, 12 6 ̈ 0 = 5 3, 9, 12 6 5 3, 9, 12 6 ́ 0 = 0

5 3, 1, 0 6 ̈ 5 0, 2, 4 6 = 506 5 4, 2, 1 6 ̈ 5 1, 2, 3, 4 6 = 5 1, 2, 3 6

5 4, 6, 8, 12 6 ̈ 5 6, 8, 14, 17 6 = 5 6, 8 6 5 2, 5, 9 6 ̈ 5 1, 2, 3, 4, 5 6 = 5 2, 5 6

A 8 C D 8 B E 8 C DhE EhA

A 8 U D 8 A 08 A 5 1, 2 68 D C 8 A

E= 5 3, 7 6 , U= 5 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 6.

A= 5 1, 3, 4, 5, 7, 8 6 , B= 5 2, 4, 6, 8 6 , C= 5 1, 3, 5, 7 6 , D= 5 1, 2, 3 6 ,

5 2, 4, 9, 12, 13 6 = 5 13, 12, 9, 4, 2 6 5 7, 11, 4 6 = 5 7, 11, 4, 0 6

7  5 2, 4, 6, 8 6 7  5 1, 3, 5, 7 6

2  5 1, 3, 5, 7, 9 6 1  5 6, 2, 5, 1 6

5  5 1, 2, 5, 8 6 6  5 1, 2, 3, 4, 5 6

APPENDIX A Sets 601