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Contemporary Mathematics (MAT-130) Set Theory (Chapter 2)

Bergen Community College Cerullo Learning Assistance Center (CLAC) 201-447-7489 Room L-125

Let:

* +

* + * + * + * +

Find:

1) ( )

2) ( )

3) What is the cardinality of D?

4) What is the cardinality of U?

5) Find the number of subsets of A

6) List the subsets of B

7) Find the number of subsets of C

8) Find the number of subsets of U

9) ( )

10) ( )

11) ( )

12) ( )

13) Find the number of proper subsets

of A


of D


of

16)

17)

18)

19)

20)

21)

22)

23)

24)

25) ( )

26)

27)

28)

29)

30) ( )

31) ( )



32) ( ) ( )

33) ( )

34) ( )

35) ( )

36) ( ) ( )

37) ( )

38) ( )

39) ( )

40) ( ) ( )

41) ( )

42) ( ) ( )

43) ( )

44) ( )

45)

46) What is the cardinality B?

47) What is the cardinality of A?

48) What is the cardinality C?


of U



Create a Venn Diagram identical to the sample provided below and shade the region

represented by:

50)

51)

52)

53)

54) ( )

55) ( ) ( )

56) ( )

57) ( ) ( )

58) ( )

59)

60) ( )

61) ( )

62) ( )

63)

64)

65) ( )



For the diagram below, use symbols to describe the following regions

(answers may vary).

66) Region I, II, V, and IV

67) Region V

68) Region II and V

69) Region VIII

70) Region I

71) Region I, II, III, IV, VI, VII, VIII

72) Region III and VI

73) Region I, II, III, VI, VII, VIII

74) Region II, III, VI

75) Region II, VI, V



76) A survey was conducted of BCC students that resulted in the following information:

50 of them are taking math, 60 of them are taking English, 20 of them are taking both

English and math and 80 of the students are taking neither:

a) How many students are taking Math only?

b) How many students are taking English only?

c) How many students are taking Math or English?

d) How many students were surveyed?

77) One hundred People were contacted and responded to a music survey. 30 people liked pop

music, 25 people liked rock music and 20 people liked classical music. 15 people liked pop

and rock, 12 people liked pop and classical music and 13 people liked classical and rock

music. Only 6 people liked all three kinds.

a) How many people liked pop music only?

b) How many people liked rock music only?

c) How many people liked classical music only?

d) How many people liked pop or rock music?

e) How many people liked pop and rock music?

f) How many people liked pop and rock but not classical music?

g) How many people liked none of the genre?

h) How many people liked at least two of the genres?

i) How many people liked only two of the genres?

78) People were contacted and responded to a food survey. 50 people liked Mexican food, 60

people liked Italian food and 45 people liked Chinese food. 10 people liked Mexican and

Italian food only. 15 people liked Chinese food only. 20 people liked Mexican and Chinese

food and 20 people liked Italian and Chinese food. 20 people liked Mexican food only. 5

people liked none of the foods being surveyed.

a) How many people liked all three types of food?

b) How many people liked Italian food only?

c) How many people liked Chinese food only?

d) How many people did not like Mexican food?

e) How many people did not like Chinese food?

f) How many people were surveyed?



Solutions:

1) 5

2) 5

3) 2

4) 8

5) 32

6) * + * + * + * + * + * + * + * +

7) 32

8)

9) 9

10) 15

11) 40

12) 64

13) 31

14) 3

15) 63

16) * +

17) * +

18) * +

19) * +

20) * +

21) * +

22) * +

23) * +

24) * +

25)

26) * +

27) * +

28)

29) * +

30) * +

31) * +

32) * +

33)

34) * +

35) * +

36) * +

37) * +

38)

39) * +



40) * +

41) * +

42) * +

43) * +

44) * +

45) * +

46) 3

47) 5

48) 5

49) 82 1 = 255

50)

51)



52)

53)

54)

55)



56)

57)

58)

59)



60)

61)

62)

63)



64)

65)

66)

67)

68)

69) ( )

70) ( )

71) ( )

72)

73) ( )

74) ( )

75) ( ) ( ) OR ( )



76)

a) 30

b) 40

c) 90

d) 170

77)



a) 9

b) 3

c) 1

d) 40

e) 15

f) 9

g) 59

h) 9 + 6 + 6 + 7 = 28

i) 9 + 6 + 7 = 22

78)

a) 10

b) 30

c) 15

d) 60

e) 65

f) 110

