Handout #1

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Set operations: page A

1. Express the resulting set given A = {1, 2, 3}, B = {4, 5, 6}, and C = {6, 7}.
a. A È B b. A Ç B c. C È B d.  C Ç B

Answer true or false given N = {1, 2, 3,..}, W = {0, 1, 2,...}, Z = {..., -1, 0, 1, ...}.
2. W Í N 3. N Í W 4. W Í Z 5. Z Í W
6. N Í  {} 7. {} Í N 8. {-1} Ç N = {Æ}

List all the subsets of the given set.
9. {a} 10. {a, b} 11. {a, b, c}

12. If  A Í B and B Í  A, then sets A and B are ________. (Fill in)

List the first four elements (in ascending order) of the given set.
13. {x: x = 3n - 5 and n Î N} 15. {x: x = 3n and Î N}
14. {x: x = 3n - 5 and n Î W} 16. {x: x = 2(5)n and n Î W}

Construct the given set or sequence.
17. {1, 3, 5, 7,...} 20. {3, 9, 27, 81,...}
18. {-2, -4, -6, -8,...} 21. {1, 3, 9, 27,...}
19. {5, 8, 11, 14,...} 22. -1, 1, -1, 1,...

 


The system of real numbers: page B

Express each number as a quotient of two integers.
1. 5 2. 1 3. 0 4. -3
5. 2 1/4 6. -4 1/3 7. 0.3 8. -3.7

Express each number as a decimal.
9. 7/10    10. 4/25 11. -2/5    12. -3/4
13. 9/15 14. -14/56 15. -7/8 16. 18/48
17. 1 9/50 18. -3 17/20 19.  -6/5 20. 11/4
21. 5/6  22. 4/11 23. -8/9 24. -1/18

Express each number as a quotient of integers in lowest terms.
25. 0.4 26. -3.6 27. -2.57 28. 0.85
29. 1.1195 30. -4.125 31. 0.0625 32. 0.00375
  
33. 0.33... 34. 0.55... 35. 0.1818... 36. 0.5454...
37. 0.312312... 38. 0.561561...  39. 5.6464... 40. 2.6868...
41. 0.166...                       42. 0.833.. 43. 3.266... 44. 4.177...
45. 0.02727...  46. 0.04242... 47. 1.38181... 48. 2.47272...
  
53. 0.99...

 

Page A ANSWERS: 1a. {1, 2, 3, 4, 5, 6}    1b. {}    1c. {4, 5, 6, 7}    1d. {6}    3. true
5. false    7. true    9. {}, {a}     11. {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}
13. {-2, 1, 4, 7,...}    15. {3, 9, 27, 81,...}     17. {x: x = 2n - 1 and n Î N}
19. {x: x = 3n + 2 and n Î N}     21. {x: x = 3n and n Î W}

Page B ANSWERS: 1. 5/1    3. 0/1     5. 9/4    7. 3/10    9. 0.7     11. -0.4    13. -0.6
15. -0.875    17. 1.18    19. -1.2     21. 0.833...     23. 0.88...    25. 2/5    27. 257/100
29. 2239/2000    31. 1/16    33. 1/3     35. 2/11    37. 104/333    39. 559/99    41. 1/6
43. 49/15    45. 3/110    47. 76/55    53. 1

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