3. C

5. A

6. E

9. ⊆

10. ⊆

12. ⊆

15. Both

18. ⊂

20. ⊂

21. Neither

24. True

25. False

27. True

30. False

33. True

36. True

39. True

40. False

42. True

45. 64, 63

48. True

50. {1, 3, 4, 6, 8}

51. {2}

54. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

55. {Higher cost, Lower cost, Educational, More time to see sights, Less time to see sights, Cannot visit relatives along the way, Can visit relatives along the way}

57. {Higher cost, More time to see the sights, Cannot visit relatives along the way}

65. {A}, {B}, {C}, {D}. {E}

69. a) 15

b) 16 there are no more bills to select

70. a) 20

b) 21 there are no more coins to select

72. Every set is a subset of itself. The empty (or null) set is a subset of every set

Mth 2.3

3. A

5. E

6.

9. Y= {a. b, c} Z= {b, c, d, e, f}

= {a, b, c, d, e, f}

10. Y= {a, b, c} Z= {b, c, d, e, f}

= {b, c}

12. Y= {a, b, c} U= {a, b, c, d, e, f, g}

= {a, b, c}

15. X= {a, c, e, g} Y={a, b, c}

= {d, f}

18. Y= {a, b, c} X= {a, c, e, g} Z= {b, c, d, e, f)

= {a}

21. Z= {b, c, d, e, f) X= {a, c, e, g} Y= {a, b, c}

= {a}

24. Y= {a, b, c} - X= {a, c, e, g}

= {b, e, g}

25. X= {a, c, e, g} (X= {a, c, e, g} Y= {a, b, c})

= {e, g}

27. X= {a, c,? e,_ g} ?Y= {a, b, c}

= {d, f}

33. The set of all elements that are in C but not in B, or are in A

35. The set of all elements that are in A, but not in C, or in B, but not in C

36. The set of all elements that are not in A or not in B, and also are not in C.

39. {L, B}

42.

45. The set of all tax returns filed in 2005 with out itemized deduction

50. Always True

51. Not always true

54. Not always true

55. a) {1, 3, 5, 2}

b) {1, 2, 3, 5}

c) for any sets X and Y, X ∪ Y = Y ∪ X

57. a) {1, 3, 5, 2, 4}

b) {1, 3, 5, 2, 4, 3}

c) for any sets X, Y & Z (X ∪ Z) = (X ∪ Y) ∪ Z

60. a) X= {1, 3, 5} Y={1, 2, 3}

= {1, 3}

b) {4}

63. True

65. False

66. False

69. True

70. True

72. A= {3, 6, 9, 12}, B= {6, 8}

A *B= {(3, 6), (3, 8), (6, 6), (6, 8), (9, 6), (9, 8), (12, 6), (12, 8)}

B*A= {(6,3), (6,6), (6,9), (6,12), (8,3), (8,6), (8,9), (8,12)}

75. n (A*B)=6: n(B*A)=6

85. The whole rectangle is shaded, with all of circle B shaded, and only the left side on circle A is not shaded

87. The whole rectangle is shaded, with all of circle A shaded and only the right side on circle B is not shaded.

90. Everything is shaded

93. Nothing is shaded

95. Nothing is shaded

2.4

3. a) 1

b) 3

c) 4

d) 0

e) 2

f) 10

g) 2

h) 5

5. n( A∩B)= n(A) + n(B) ?n(A ∪ B)

= 8 + 14 -5

= 17

6. n(A∪ B)= n(A) =16, n(B)= 28, & n( A∩ B)=9

= 16 + 28- 9

= 35

9. n(A) = n(B) + n(A ∩ B) ?n(A∪B)

= 55 + 15 ?35

= 35

10. n(B)= n(A) + n(A ∩ B) ?n(A ∪ B)

= 20 + 6 ?30

= -4

15. 16 is just in the A circle. 14 is just in the B circle. 18 is just in the C circle. 20 is in both the A and B circle. 6 is in both the A and C circle. 10 is in both the B and C circle. 15 is in all three circles.

20. a) 3

b) 2

c) 10

21. a) 18

b) 15

c) 20

d) 5

24. a) 0

b) 4

c) 3

d) 0

e) 6

25. a) 37

b) 22

c) 50

d) 11

e) 25

f) 11

27. a) 31

b) 24

c) 11

d) 45

30. a) 170

b) 7

c) 14

You need to run the qa and query programs for these assignments and submit the SEND files. Having done the problems, and now being acquainted with how to submit SEND these files, this should not be difficult.