A-1 ToThe Student In this section we provide the answers that we think most students will obtain when they work the exercises using the methods explained in the text. If your answer does not look exactly like the one given here, it is not necessarily wrong. In many cases there are equivalent forms of the answer. For example, if the answer section shows 3 4 and your answer is 0.75, you have obtained the correct answer but written it in a different (yet equivalent) form. Unless the directions specify otherwise, 0.75 is just as valid an answer as 3 4 . In general, if your answer does not agree with the one given in the text, see whether it can be transformed into the other form. If it can, then it is the correct answer. If you still have doubts, talk with your instructor. Chapter R Review of Basic Concepts R.1 Exercises 1. true 3. false; This is an improper fraction. Its value is 1. 5. C 7. 1 2 9. 5 6 11. 3 5 13. 1 5 15. 5 6 17. 1 5 7 19. 6 5 12 21. 13 5 23. 38 3 25. 24 35 27. 1 20 29. 6 25 31. 6 5, or 1 1 5 33. 9 35. 65 12 , or 5 5 12 37. 14 27 39. 10 3 , or 3 1 3 41. 12 43. 1 16 45. 10 47. 18 49. 35 24 , or 1 11 24 51. 84 47 , or 1 37 47 53. 11 15 55. 2 3 57. 8 9 59. 29 24 , or 1 5 24 61. 107 144 63. 43 8 , or 5 3 8 65. 5 9 67. 2 3 69. 1 4 71. 17 36 73. 67 20 , or 3 7 20 75. 32 9 , or 3 5 9 77. (a) 1 2 (b) 1 4 (c) 1 3 ; 1 6 79. (a) 6 (b) 9 (c) 1 (d) 7 (e) 4 81. (a) 46.25 (b) 46.2 (c) 46 (d) 50 83. 4 10 85. 64 100 87. 138 1000 89. 43 1000 91. 3805 1000 93. 143.094 95. 25.61 97. 15.33 99. 21.77 101. 81.716 103. 15.211 105. 116.48 107. 739.53 109. 0.006 111. 7.15 113. 2.8 115. 2.05 117. 1232.6 119. 5711.6 121. 94 123. 0.162 125. 1.2403 127. 0.02329 129. 1% 131. 1 20 133. 12 1 2 %, or 12.5% 135. 0.25; 25% 137. 1 2 ; 0.5 139. 3 4 ; 75% 141. 4.2 143. 2.25 145. 0.375 147. 0.5; 0.556 149. 0.16; 0.167 151. 0.54 153. 0.07 155. 1.17 157. 0.024 159. 0.0625 161. 79% 163. 2% 165. 0.4% 167. 128% 169. 40% 171. 51 100 173. 3 20 175. 1 50 177. 7 5 , or 1 2 5 179. 3 40 181. 80% 183. 14% 185. 18.18% 187. 225% 189. 216.6% R.2 Exercises 1. subset 3. intersection 5. infinite 7. 54, 56 9. 515, 16, 17, 18, 21, 506 11. finite; yes 13. infinite; no 15. infinite; no 17. infinite; no 19. 512, 13, 14, 15, 16, 17, 18, 19, 206 21. E1, 1 2 , 1 4 , 1 8 , 1 16 , 1 32F 23. 517, 22, 27, 32, 37, 42, 476 25. 59, 10, 11, 12, 13, 146 27. ∈ 29. ∉ 31. ∈ 33. ∉ 35. ∉ 37. ∉ 39. false 41. true 43. true 45. true 47. false 49. true 51. true 53. true 55. false 57. true 59. true 61. false 63. ⊆ 65. s 67. ⊆ 69. true 71. false 73. true 75. false 77. true 79. true 81. 50, 2, 46 83. 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 136 85. ∅; M and N are disjoint sets. 87. 50, 1, 2, 3, 4, 5, 7, 9, 11, 136 89. Q, or 50, 2, 4, 6, 8, 10, 126 91. 510, 126 93. ∅; ∅ and R are disjoint. 95. N, or 51, 3, 5, 7, 9, 11, 136; N and ∅ are disjoint. 97. R, or 50, 1, 2, 3, 46; M and N are disjoint. 1M¨N2 and R are disjoint. 99. 50, 1, 2, 3, 4, 6, 86 101. R, or 50, 1, 2, 3, 46 103. ∅; Q′ and 1N′ ¨U2 are disjoint. 105. 51, 3, 5, 7, 9, 10, 11, 12, 136 107. M, or 50, 2, 4, 6, 86 109. Q, or 50, 2, 4, 6, 8, 10, 126 111. 1, 3 113. -6, - 12 4 1or -32, 0, 1, 3 115. - 13, 2p, 112 R.3 Exercises 1. 6 (or is less than) 3. negative 5. base; exponent 7. 1000 9. 4 11. 10 13. - 4 7 15. -3 17. true 19. false 21. true 23. true 25. false 27. -19 29. -9 31. 9 33. - 19 12 35. 1.7 37. -5 39. -11 41. 21 43. -10.18 45. 67 30 47. 14 49. -6 51. 40 53. -35 55. 0 57. 6 5 59. 1 61. 0.4 63. -0.024 65. -7 67. 6 69. -4 71. 0 73. undefined 75. 25 102 77. - 9 13 79. -9 81. -16 83. 16 85. -243 87. -162 89. -6 91. -60 93. -12 95. - 25 36 97. - 6 7 99. 28 101. - 1 2 103. - 23 20 105. - 25 11 107. - 11 3 109. - 13 3 111. 6 113. distributive property 115. inverse property 117. identity property 119. commutative property 121. associative property 123. closure property 125. no; For example, 3 - 5≠5 - 3. 127. 20z 129. m+ 11 131. 2 3 y + 4 9 z - 5 3 133. 18 - 142p = -6p Answers to Selected Exercises
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