The Real Number System

Solution Set 1

1.
a. Integers`={-3,4,11,57}` b. Rational Numbers`={-3,4,1/5,11,3.14,57}` c. Irrational Numbers`={0.25225222522225...}`
d. Real Numbers`={`All are real numbers`}` e. Prime Numbers`={11}` f. Composite Numbers`={4,57}`
2.
a. Integers`={21,53}` b. Rational Numbers`={5.bar17,-4.25,-1/4,21,53,0.45454545...}` c. Irrational Numbers`={pi}`
d. Real Numbers`={`All are real numbers`}` e. Prime Numbers`={53}` f. Composite Numbers`={21}`
3. `A={4,6,8,9,10}` 4. `B={2}` 5. `C={53,59}` 6. `D={4}`
7. `{2,4,6,8}` 8. `{0,1,2,3}` 9. `{3,5,7,9}` 10. `{-1,0,3,8}`
11. `{0,1,2,3}` 12. `{2,4,6,8}` 13. `{1,3}` 14. `{1,3}`
15. `{1,3}` 16. `{O/}` 17. `{0,2,4}` 18. `{6,10}`
19. `{0,1,2,3,4,5,11}` 20. `{0,1,2,3,4,6,10}` 21. `{1,3}` 22. `{3}`
23. `{O/}` 24. `{0,1,2,3,4,5,6,10,11}` 25. Assocative Property of Addition
26. Commutative Property of Addition 27. Identity Property of Multiplication 28. Symmetric Property of Equality
29. Reflexive Property of Equality 30. Substitution Property of Equality 31. Transitive Property of Equality
32. Distributive Property 33. Inverse Property of Addition 34. Inverse Property of Multiplication
35. Commutative Property of Addition 36. Commutative Property of Multiplication 37. Transitive Property of Equality
38. Distributive Property 39. `(-3a)/7` 40. `(29a)/35` 41. `(-7a)/20` 42. `69/40a` 43. `(-10)/21`
44. `(-154)/231` 45. `(-18)/5` 46. `6/55` 47. `(-2a)/15` 48. `(1-6a)/2a` 49a. `26/55` of the pool.
49b. `(26x)/165` of the pool. 50. `-25/4` 51. `8/59` 52. `(-5)/22` 53. `3-2!=2-3`
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ 1!=-1`
54. `1-:2!=2-:1`
`\ \ \ \ \ \ \ \ \ \ \ \ 1/2!=2`
55. `(7-4)-6!=7-(4-6)`
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -3!=9`
56. `(12-:4)-:2!=12-:(4-:2)`
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3/2!=6`
57. False 58. True 59. True 60. False
61. False 62. False 63. True 64. False 65. True 66. True
67a. `0.bar72` 67b. `0.825` 67c. `.bar285714` 67d. `.bar135` 68. `22/7` is closer
69. `(sqrt(x+9)-3)/x` is approaching `0.bar16` or `1/6` 70. `(1/2-1/(x+2))/x` is approaching `0.25` or `1/4`
71. All the properties except Identity Property of Addition and the Inverse Properties. 72. All the properties except for Inverse Property of Multiplication.
73. All the properties. 74. All the properties except the Identity Properties. 75a. `5+7` 75b. `23+7` 76. `3` and `5`, `5` and `7`, `11` and `13`, `17` and `19`, `41` and `43`.