208
บทเรียนสําเร็จรูปวิชาคณิตศาสตร์ ชั ้นมัธยมศึกษาปี ที 4 โดย... นางมุกดา ภักดีพันธ์ โรงเรียนท่าแซะรัชดาภิเษก จังหวัดชุมพร สํานักงานเขตพื้นที ่การศึกษาชุมพร เขต 1 เรื อง

Set

Embed Size (px)

Citation preview

  • 1. 4... 1

2. 4... 1 3. 4 2544......... 4. 1. 42. 3. 4. 5. 6. 7. 5. .1....... 16 17 1. .18 1.1 201.2 (element) 371.3 .421.4 ..53 1.5 571.6 ..68 6. ( ) 2. 743. 814. 1035. - 1096. 123 6.1 ..125 6.2 129 6.3 ... 133 6.4 ..137 6.5 .. 149 7. ( ) 7. . 163 184 .199.. 200 8. (1) (2) . . . . . . . . 9. (3) B (4) C={x | x , 3x 32 } 100 B C . {10}. {-10, 10} . {2, 4, 6, }. {50}. {2, 4, 6, 8, 10}. {-50, 50} . {2, 4, 6, ,30 } . { , -4, -2, 0, ,10} 10. (5) D = {1, 2, 3, 4, 5} (6) E = {-2, 2} D E . {x | x I+, x < 6} . {x | x2 + 3 = 7 } . {x | x I, x < 6}. {x | 2x2 + x = 2 } . {x | x I, 1 < x < 5 } . {x | 4x2+ x = 18 } . {x | x I, 1 < x < 6 } . {x | 5x2 5x = 10 } 11. (7) (8) . {x | x I, x < 1} A ={x | x N, 0x 1}. {x | x I+, x < 1}B ={x | x P, x }. {x | x I, x < 1}C ={x | x I, x 0}. {x | x I+, x 1}D ={x | x I, x2 0} . A = . B = . C = . D = 12. (9) (10) . { , 0 , 1, 2 }. {x | x N, 2x 0}. { 0, 1, 2, 3, }. {x | x I, x2 > 0 }. { , 0, 1, 2, }. {x | x I+, x2 x >0}. { 0, 1, 2, , 100 }. {x | x I, 2x2 + x = 0} 13. (11) (12) . {x | x I, x 10}A = {x | x I, 1 < x < 2}. {x | x I+, x < 1 } B = {x | x I, 1 x 2}. {x | x I, x > 1 } C = {x | x I, x > 5}. {x | x I ,1 < x 9 }C ={x | x } C = {x | x 9 = 1}D ={x | x } D = {x | x = 100 } . A = C . A = B . A = D . B = C . B = C . A = C . B = D . C = D 15. (15) U = {1, 2, 3, ,9}(16) {0,{5},6}A = {x | x2 = 100}. {{0}, 5, 6} . {0,{5}} . A = {10}. {5, 6} . A = {50}. {5} . A = { } . A = {-10, 10} 16. (17) A = {1, { 2, 5 }} (18) B = {4, 5, 6} B . {1} A . 4 . {1, 2} A. 8 . {2, 5} A. 12 . {1, 2, 5} A . 16 17. (19) A = {{2}} P(A) (20) A = {, 1, 2} P(A) . {{2}}. {{1}} . {, 2} . {{2}} . {, {2}} . {, 1}. {, {{2}}}. {{, 1, 2}} 18. (21) n (P(A)) = 32 n(A) (22) U . 4 A . 5 B . 6 C . 16 . A ={1, 2}, B ={2, 3}, C ={1, 2, 3, 4} . A ={1, 2}, B ={3, 4}, C ={1, 2, 3, 4} . A ={1, 2}, B ={2}, C ={1, 2, 3, 4} . A ={2}, B ={3}, C ={1, 2, 3, 4} 19. (23)U 24U = {-4, -3, -2, , 9}A = {-2, 1, 7, 9} A BB = {-3, 0, 1, 4, 9} C(24) AB . {-3, -2, 0, 1, 4, 7, 9} . {1, 7, 9} . A C, C B A C =. {1, 9} . C A, C B A B =. { } . A C, B C A B = . B A, B C A C = 20. 25 26U = {-4, -3, -2, , 9}A = {-2, 1, 7, 9}B = {-3, 0, 1, 4, 9}(25) AB (26) A . {-3, -2, 0, 1, 4, 7, 9} . {-4, -3} . {1, 4, 7, 9}. {0, 2, 3, 5, 6, 8} . {1, 7, 9} . {-4, -3, -1, 0, 2, 3, 4, 5, 6, 8} . {1, 9}. {-4, -3, -1, 0, 2, 3, 4, 5, 6, 8, 9} 21. 27 (28) n (U) = 60 U = {-4, -3, -2, , 9} n (A) = 10A = {-2, 1, 7, 9}n (B) = 5B = {-3, 0, 1, 4, 9} n ( AB) = 2 n ((AB)) (27) A B . 13 . {-3, -2, 0, 1, 4, 7, 9}. 45 . {-2, 7}. 47 . {7, 9} . 49 . {-2} 22. (29) 9 16 15 50 10 23 81232 13 10 U 100 . 13(30) . 15 . 22 . 8. 23 . 12. 14. 17 23. 1 1. 2. (Venn-Euler Diagram) 24. 1 2( SET ) 1) 2) 3) 4) 5) 25. 31 ( SET ) (George Cantor) 19 ( George Cantor. 2008, Online)(, 2547:1) 26. 41.1 (, 2547:1) 27. 5 8 ...(1) ( . 2551, ) ? ? (2) 28. 6 5 (1) (2) ......... 29. 7 ... (1) ..................................................................(2) ? ? (3) 30. 7 8(1) (2) (3) ......... 31. 9 1, 2, 3, ......................(1) ......................................................................(2) 0 ? ? (3) 32. 9 10 (1) (2) (3) 0 0 ......... 33. 11 ? ? 34. 12 .................................................................................................... 35. 13 12 ......... 36. 14 ............................(1).....................................................................................................(2) 37. 15 14(1) (2) ......... 38. 16 ............................(1).....................................................................................................(2) 39. 17 16 (1) (2) ......... 40. 18 ...... (1) ...... (2) ...... (3) ...... (4) ...... (5) 5 ... 41. 19 18(1) (2) (3) (4) (5)...... 42. 20...... ... 43. 1.2 (element) 21 (, 2547:1) ...... ? 44. 22 21 45. 23 (, 2547:2) 46. A = { 1, 2, 3 } 24 1 A 1 A 2 A 2 A 3 A ........(1)4 A 4 A 5 A ........(2) 47. 25 24(1) 3 A(2) 5 A ... 48. 261.3 2 49. 1 27 ( , ) (, 2547:1) 1) {1 , 2 , 3 , 4 , 5}2) {, , , }3){, , } 50. 28 1) {1 , 2 , 3 , }2) {a, b, c, , z} (...) {1, 2, 9, , 100} 9( , 2545 :3) 51. 29 A, B, C a, b, c (, 2547:1) 1) A = {1, 2, 3} 2) B ={m, n, o} 52. 2 30 (, 2547:2) A = {x | x } 53. 31 B B ... (1) ...(2) ? 54. 32 31(1) B ={, , , , }(2) B ={x | x } 55. 33 (1) (2) 3(3) -4(4) 11 20(5) 70... ( , ) 56. 34 33 (1) {} (2) {1, 2} (3) {-3, -2, -1} (4) {12, 13, 14, , 19} (5) {71, 72, 73, } ...... 57. 35 (1) { , , } (2) {1, 2, 3} (3) {-4, -3, -2, -1} (4) {10, 11, 12, , 99} (5) {, 5, 10, 15, }... 58. 36 35(1) {x | x } (2) {x | x 4}(3) {x | x -5 0}(4) {x | x } (5) {x | x 5 } 59. 371.4 Empty set Null set { } 60. 38 A = {x | x 2 3} 2 3 A (, 2547:2) 61. 39 (1) A = {x | x } (2) B = {x | x 0} (3) C = {x | x 2}(4) D = {x | x 2 } (5) E = {x | x 9 10 } ... 62. 40 39 (1) (2) 0 (3) 2 0, -2, -4, (4) 2 2 (5) 9 10 ...... 63. 1.5 41 ( finite set ) (, 2547:2) A = {0, 2, 4, 8} A 4 A 64. 42 (Infinite set) (, 2547:3) A = {0, 2, 4, 6, ...} A A 65. 43 1) 2) {, , } 66. 443) I I+ I- N P 67. 45 I = { ,-3, -2, -1, 0, 1, 2, 3, } I = {0, 1, 2, 3, } I = {0, -1, 1, -2, 2, } 68. 46 I+ = {1, 2, 3, } I- = {-1, -2, -3, } N = {1, 2, 3, } P = {2, 3, 5, 7, } 69. 47 A = { x| x 6 } A = { x| xN , x < 6 } 70. 48 (1) {2468}(2) {a, bb, ccc, dddd}(3) {1, 3, 5, , 19 }(4) {x | x } (5) {x | x 6 7 } 71. 49 48(1) 1 (2) 4 (3) 10 (4) 4 (5) 0 72. 50 (1) {-2, -4, -6, -8}(2) {0, 1, 2, , 100}(3) {, 0, 1, 2, 3}(4) {x | x N , x > 6 }(5) {x | x I+ , x < 0} ... 73. 51 50 (1) (2) (3) (4) (5) ........ .. 74. 52 1.6 (equal set or identical set) A = {1, 2, 3 } B = {1, 2, 3, } D = {2, 3, 4 }C = {2, 3, 1 } 75. 53 A C A C A B D 76. 54 A B A B B A(, 2547:3) A= B 77. 55 A B A B B A (, 2547:3) AB 78. 56 (1) A = {-2, -4, -6, -8}, B = {-8, -6, -4, -2}(2) C = {0, 1, 2, , 100}, D = {x | x 101}(3) E = {x | x }(4) F = {x | x }(4) G = {5, 10, 15, }, H = {x | x = 5n n N}(5) J = {x | x I , x2=100}, K = {10}... 79. 57 56(1) A=B(2) CD(3) E=F(4) G=H(5) J K 80. 58 2 (Relative Universe) 6) 81. 59 2 (Relative Universe) U (, 2547:7) 82. 60 U A = {x | x < 5} A = {1, 2, 3, 4} 83. 61 U A = {x | x < 5}A = { , 1, 2, 3, 4} A = {4, 3, 2, } 84. 62 R A = {x | x2 = 25} A = {-5, 5} 25 -5 5 85. 63 (1) U = { x | x N }, A = {x | x2 = 64}(2) U = { x | x I }, B = {x | x < 4}(3) U = { x | x I}, C = {x | x > 3}(4) U = { x | x P}, D = {x | x 15}N I I P 86. 64 63(1) A = {8}(2) B = {3, 2, 1, }(3) C={ }(4) D = {2, 3, 5, 7, 11, 13} 87. 653 (Subsets) 7) 8) 88. 66 3 (Subsets) A B A B A B A B A B A B (, 2547:7) 89. 67 A = {1, 2, 3, 4, 5 } A (1) B = {1, 2, 3 }(2) C = {2, 3, 6 } (3) D = {4 }(4) E = {1, 4, 7 } (5) F = {5 } ... A B A B 90. 68 67(1) B A B A(2) C A 6 C A(3) D A D A(4) E A 7 E A(5) F A F A 91. 69 A = {1} A {1} {} 2 92. 70 B = {1, 2} B {1} {2} {1, 2} {} 4 93. 71 C = {1, 2 , 3} C {1}{2} {3}{1, 2} {1, 3} {2, 3} {1, 2, 3} {} 8 94. 72 D ={1, 2, 3, 4} D {1}{2}{3}{4} {1, 2} {1, 3}{1, 4}{2, 3}{2, 4}{3, 4}{1, 2, 3}{1, 2, 4}{1, 3, 4}{2, 3, 4} {1, 2, 3, 4}{} 16 95. 73 E = {1, 2, 3, 4 , 5} E {1}{2} {3} {4}{5} {1, 2} {1, 3}{1, 4}{1, 5} {2, 3}{2, 4}{2, 5}{3, 4}{3, 5} {4, 5} 96. 74{1, 2, 3}{1, 2, 4} {1, 2, 5}{1, 3, 4}{1, 3, 5}{1, 4, 5}{2, 3, 4}{2, 3, 5}{2, 4, 5}{3, 4, 5}{1, 2, 3, 4}{1, 2, 3, 5} {1, 2, 4, 5}{1, 3, 4, 5} {2, 3, 4, 5} {1, 2, 3, 4, 5}{} 32 97. 75 1) A A A 2) 3) A B B A A = B 98. 76 1 2 21 2 4 22 3 8 23 416 24 5 (1).(3) 6 ...(2).(4) n.(5) 99. 77 76(1) 32(2) 64(3) 25(4) 26(5) 2n 100. 78 A n A 2n 1) A 10 A 2102) A 25 A 225 101. 79 A n(A) A = {0, 2, 4} n(A) = 3 102. 80 A = {0, {1, 2 }}n(A) = 2 A 0 {1, 2} A 22 4 {0} {{1, 2}}... {0,{1, 2}}{} 103. 81 1 1 {0, {1, 2}} 0, 1, 2 ... 104. 82{{1, 2} } 0 {0} 0 , 1, 20, 1, 21, 2 {}{0,{1, 2} } {0, {1, 2}} 105. 83 B = {1,{3, 5, 7}} n(B) =.(1) B ........(2) B .....................(3) 106. 84 83(1) 2(2) 4(3) {1}, {{3, 5, 7}}, {1, {3, 5, 7}}, { } .... 107. 85 A = {0, {1, 3 }, 5 } (1) {1} A (5) {0, 5} A (2) {1, 3} A(6) {5} A (3) {{1, 3}} A(7) {{3}} A (4) {0, 3} A (8) { } A 108. 86 85(1) (5) (2) (6) (3) (7) (4) (8) .... 109. 874 9) 110. 4 88 A A AP(A) 111. 89 A = {1, 2} A {1} {2}{1, 2} {} P(A) = { {1}, {2}, {1, 2},{ }} 112. 90 B = {1 ,{3 , 5 }} n(B) = 2 B {1}{{3, 5}}{1,{3, 5}} {} P(B) = { {1}, {{3, 5}} , {1,{3, 5}},{ }} 113. 91 (1) A = {a, b } (2) B = {-1, 0, 1 } (3) C = {{1, 3}, 5} 114. 92 91 (1) P(A) = {{a}, {b}, {a, b}, } (2) P(B) = {{-1}, {0}, {1}, {-1, 0}, {-1, 1}, {0, 1}, {-1, 0, 1}, } (3) P(C) = {{{1, 3}}, {5}, {{1, 3}, 5}, } 115. 93 -5 (Venn-Euler Diagram) 10) 116. 5 - 94 (Venn-Euler Diagram) - (John Venn) ( Leonhard Euler and John Venn. 2008, Online) (Leonhard Euler)( , 2545:15) 117. 95 - (Venn-Euler Diagram 1. 2. 118. A B 96 4 U 1)AB A B (disjoint sets) 119. U = {1, 2, 3, ,10} 97 A = {3, 4, 5 } B = {6, 7}UAB 120. 98 U2)A B A B 121. U = {1, 2, 3, ,10} 99 A = {3, 4, 5 } B = {3, 5, 7} UA B 122. 100UA3)B A B A B 123. U = {1, 2, 3, ,10} 101 A = {3, 4 }B = {3, 4, 5 } UA B 124. 102 U = {1, 2, 3, ,10} A = {1, 2, 3, 4, 5 } B = {4, 5 }UBA 125. 103 A BU4) A = B 126. U = {1, 2, 3, ,10} 104 A = {1, 2, 3}B = {x | x < 4 }A BU 127. 105 U A = {1, 2, 3,, 10 }B = {3, 5, 7}C = {6, 8, 10, 12} 128. 106 93 UBAC....... 129. 1076 (Operation of sets) 11) 12) 13) 14) 15) 130. 108 6(Operation of sets) 4 1) (Union) 2) (Intersection) 3) (Complement) 4) (Difference of sets) 131. 1096.1 A B A B ABAB = {x| xA xB x } 132. 110A = {1, 2, 3, 4}B = {3, 4, 5 } C = {1, 2, 3, 4, 5 } C A B 133. C A 111 B C A B 134. 112 ABU A B AB 135. 1136.2 A B A B ABAB = {x| xA xB } 136. 114A = {1, 2, 3, 4}B = {3, 4, 5 } D = {3, 4} D A B 137. 115 D A B D A B 138. 116 AB UA B AB 139. 1176.3 U A A U A A A = {x| x U x A } 140. 118 U = {1, 2, 3, , 10} A = {3, 4, 5 } E = {1, 2, 6, 7, 8, 9, 10} E A U 141. 119 E U A E A 142. 120 AU A A 143. 121 6.4 A B 144. 1221) A B A B AB A B 2) B A B A BA B A AB = {x| x A x B } BA = {x| x B x A } 145. 123 A = {1, 2, 3, 4} B = {3, 4, 5 } F = {1, 2} F A B 146. F A 124 B F A B 147. A = {1, 2, 3, 4} 125B = {3, 4, 5 } G = {5} G A B 148. G B 126 A G B A 149. 127 AB UAB AB 150. 128 BA UAB BA 151. 129 U = {-2, -1, 0, 1, 2, 3,, 20}, A = { 1, 2, 3,, 10 },B = {-2, 0, 2, 4 } C = {1, 3, 5}1. .(1.1) AB .(1.2) AB (1.5) .(1.3)A .(1.4) AB.....(1.5) (AB)(BC) 152. 1302. .(2.1) AB (2.2) (AB)C 153. 131 129 (1.1) {-2, 0, 1, 2, 3,, 10} (1.2) {2, 4} (1.3) {-2, -1, 0, 11, 12, 13, , 20} (1.4) {1, 3, 5, 6, 7, 8, 9, 10} (1.5) { 6, 7, 8, 9, 10 } 154. 132 130 U C (2.1) A B U C (2.2) A B 155. 6.5 133 A n(A) A = {, , } n(A) = 3 AB = {7, 9, 11, 15} n(AB) = 4 156. 134 A = {3, 4, 5}B = {4, 5, 6, 7} AB = {3, 4, 5, 6, 7} AB = {4, 5 }n(A) = 3 n(B) = 4n(AB) = 5 n(AB) = 2 5 = 3+4-2 157. 135A = {-2, 0, 2, 4, 6, 8 }B = {1, 2, 3, 4} AB = ..(1) AB = ..(2)n(A) = 6n(B) = 4 n(AB) = ..(3)n(AB) = ..(4) = +-(5) 158. 136 135 (1) {-2, 0, 1, 2, 3, 4, 6, 8} (2) {2, 4} (3) 8 (4) 2 (5) 8 = 6 + 4 2 159. 137 A B n(AB) = n(A) + n(B) n(AB) 160. A B 138 n(AB) = n(A) + n(B) n(AB) n(A) = 50, n(B) = 30 n(AB) = 18 n(AB) n(AB) = n(A) + n(B) n(AB) n(AB) = 50 + 30 (1) = (2) 161. 139 138 (1) 18 (2) 62 162. n(AB) = n(A) + n(B) n(AB) 140 n(U) = 100n(A) = 60n(B) = 35 n(AB) = 10 A-BA (AB)50 4015 n(A) n(AB)n(U) n(A)n(U) n(AB) 163. 141 n(U) = 100 n(A) = 40 n(B) = 35n(AB) = 8 A-BB-A ABAB(AB) (1)(2) (3) (4)(6) (5) n(A) n(AB) n(U) n(A)n(U) n(AB) 164. 142 141(1) 32(2) 27(3) 67 (4) 60 (5) 65 (6) 33 165. 143 A, B C ABC n(A) + n(B) +n(C) n(AB) n(AC) n(BC) + n(ABC) 166. 144 UA B C AB AC BC ABC 50 252030 121510 5n(ABC) = 25 + 20 + 30 12 15 10 + 5 ... = 43 167. 145 UA B C AB AC BC ABC 100 403530 152010 5 n(ABC) = (1) + (2) + (3) (4) (5) (6) + (7)......= (8) 168. 146 145(1) 40 (2) 35 (3) 30 (4) 15 (5) 20 (6) 10 (7) 5(8) 65 169. 1477 16) 170. 1487 171. 149 .4 100 35 40 15 (1) (2) 172. 150 A B AB n (A) = 35n(B) = 40n(AB) = 15 173. 151 (1) AB n (AB) = n (A) + n(B) n(AB)= 35 + 40 15= 60 174. 152 (2) AB n (AB) = n (A) n(AB)= 35 15= 20 175. 153 AB40UAB 20 15 25AB 176. .4 180 154 90 105 155 (1) (2) 177. 155 A B AB n (A) = 90n(B) = 105 n(AB) = 155 178. 156(1) AB n (AB) = n (A) + n(B) n(AB) n (AB) = n(A) + n(B) n(AB) = 90 + (1) (2)= (3) 179. 157 156 (1) 105 (2) 155 (3) 40 180. 158 (2) BA n (B A) = n(B) n(AB) = (1) (2) = (3) 181. 159 158 (1) 105 (2) 40 (3) 65 182. 160 154 U BA 90 xx105 x AB x = n(AB) 183. 161 x n (AB) = n (A) + n(B) n(AB) 155 = 90 + 105 x x = 90 + (1) (2)= (3) 184. 162 161 (1) 105 (2) 155 (3) 40 185. .4 163100 30 15 45 10 35 12 8 186. 164 26 421 8 1972 13 U 187. 165 = 13 + 21 + 26 = 60 188. 166 100 (1) 15 1225 15 810(2) 7 U (3) 189. 167 166(1) 47(2) 27(3) 8 190. (1) (2) . . . . . . . . 191. (3) B (4) C={x | x , 3x 32 } 100 B C . {10}. {-10, 10} . {2, 4, 6, }. {50}. {2, 4, 6, 8, 10}. {-50, 50} . {2, 4, 6, ,30 } . { , -4, -2, 0, ,10} 192. (5) D = {1, 2, 3, 4, 5} (6) E = {-2, 2} D E . {x | x I+, x < 6} . {x | x2 + 3 = 7 } . {x | x I, x < 6}. {x | 2x2 + x = 2 } . {x | x I, 1 < x < 5 } . {x | 4x2+ x = 18 } . {x | x I, 1 < x < 6 } . {x | 5x2 5x = 10 } 193. (7) (8) . {x | x I, x < 1} A ={x | x N, 0x 1}. {x | x I+, x < 1}B ={x | x P, x }. {x | x I, x < 1}C ={x | x I, x 0}. {x | x I+, x 1}D ={x | x I, x2 0} . A = . B = . C = . D = 194. (9) (10) . { , 0 , 1, 2 }. {x | x N, 2x 0}. { 0, 1, 2, 3, }. {x | x I, x2 > 0 }. { , 0, 1, 2, }. {x | x I+, x2 x >0}. { 0, 1, 2, , 100 }. {x | x I, 2x2 + x = 0} 195. (11) (12) . {x | x I, x 10}A = {x | x I, 1 < x < 2}. {x | x I+, x < 1 } B = {x | x I, 1 x 2}. {x | x I, x > 1 } C = {x | x I, x > 5}. {x | x I ,1 < x 9 }C ={x | x } C = {x | x 9 = 1}D ={x | x } D = {x | x = 100 } . A = C . A = B . A = D . B = C . B = C . A = C . B = D . C = D 197. (15) U = {1, 2, 3, ,9}(16) {0,{5},6}A = {x | x2 = 100}. {{0}, 5, 6} . {0,{5}} . A = {10}. {5, 6} . A = {50}. {5} . A = { } . A = {-10, 10} 198. (17) A = {1, { 2, 5 }} (18) B = {4, 5, 6} B . {1} A . 4 . {1, 2} A. 8 . {2, 5} A. 12 . {1, 2, 5} A . 16 199. (19) A = {{2}} P(A) (20) A = {, 1, 2} P(A) . {{2}}. {{1}} . {, 2} . {{2}} . {, {2}} . {, 1}. {, {{2}}}. {{, 1, 2}} 200. (21) n (P(A)) = 32 n(A) (22) U . 4 A . 5 B . 6 C . 16 . A ={1, 2}, B ={2, 3}, C ={1, 2, 3, 4} . A ={1, 2}, B ={3, 4}, C ={1, 2, 3, 4} . A ={1, 2}, B ={2}, C ={1, 2, 3, 4} . A ={2}, B ={3}, C ={1, 2, 3, 4} 201. (23)U 24 U = {-4, -3, -2, , 9} A = {-2, 1, 7, 9} A B B = {-3, 0, 1, 4, 9} C(24) AB . {-3, -2, 0, 1, 4, 7, 9} . {1, 7, 9} . A C, C B A C =. {1, 9} . C A, C B A B =. { } . A C, B C A B = . B A, B C A C = 202. 25 26U = {-4, -3, -2, , 9}A = {-2, 1, 7, 9}B = {-3, 0, 1, 4, 9}(25) AB (26) A . {-3, -2, 0, 1, 4, 7, 9} . {-4, -3} . {1, 4, 7, 9}. {0, 2, 3, 5, 6, 8} . {1, 7, 9} . {-4, -3, -1, 0, 2, 3, 4, 5, 6, 8} . {1, 9}. {-4, -3, -1, 0, 2, 3, 4, 5, 6, 8, 9} 203. 27 (28) n (U) = 60 U = {-4, -3, -2, , 9} n (A) = 10A = {-2, 1, 7, 9}n (B) = 5B = {-3, 0, 1, 4, 9} n ( AB) = 2 n ((AB)) (27) A B . 13 . {-3, -2, 0, 1, 4, 7, 9}. 45 . {-2, 7}. 47 . {7, 9} . 49 . {-2} 204. (29) 9 16 15 50 10 23 81232 13 10 U 100 . 13(30) . 15 . 22 . 8. 23 . 12. 14. 17 205. 111 21 212 22 313 23 414 24 515 25 616 26 717 27 818 28 919 29 1020 30 206. . (2545). - .4 1 : , . (2545). 2544 : , . (2546). 1 4 : , . (2547). 1 4 : 207. . (2551). [ ]. : http://www.geocities.com 2008.George Cantor. [Online]. Available from : http://www.4dlab.net 2008.Leonhard Euler and John Venn. [Online]. Available from : http://www.answers.com 2008.