離散数学 第 4回 集合の記法 (1)：外延的記法と内包的記法
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- こうご そや
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1 4 (1) :28 ( ) (4) / 35
2 () 1 (1) (4 8 ) 2 (2) (4 15 ) 3 (3) (4 22 ) () (4 29 ) () (5 6 ) 4 (1) (5 13 ) 5 (2) (5 20 ) 6 (4) (5 27 ) 7 (1) (6 3 ) (6 10 ) ( ) (4) / 35
3 () 8 (2) (6 17 ) () (6 24 ) () (7 1 ) 9 (1) (7 8 ) 10 (2) (7 15 ) 11 (3) (7 22 ) 12 (5) (7 29 ) 13 (3) (8 5 ) (8 12 ) ( ) (4) / 35
4 6 10 ( ) 6 A201 1 (4 8 ) 6 (5 27 ) A4 1 ( ) min{100, + } ( ) (4) / 35
5 ( ) 2 1 ( ) 2 ( ) (4) / 35
6 ( ) () ( ) (4) / 35
7 ( ) (4) / 35
8 ( ) { } {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} {,,,, } 1 1 ( ) (4) / 35
9 x A x A x A x A A = {,,,, } A A A A ( ) (4) / 35
10 (1) U = {,,,,,,,,,,,,,,,,,,,,,,, } = ( ) (4) / 35
11 (2) U = {x x (2014 ) } {x x () } : ; ( ) (4) / 35
12 A = {2, 3, 5, 7} = {7, 2, 5, 3} = {n n 10 } { = n n } n 4 17n n 2 247n = 0 () ( ) (4) / 35
13 A = {2, 3, 5, 7} = {7, 2, 5, 3} = {n n 10 } { = n n } n 4 17n n 2 247n = 0 () ( ) (4) / 35
14 A = {2, 3, 5, 7} = {7, 2, 5, 3} = {n n 10 } { = n n } n 4 17n n 2 247n = 0 () ( ) (4) / 35
15 A = {2, 3, 5, 7} = {7, 2, 5, 3} = {n n 10 } { = n n } n 4 17n n 2 247n = 0 () ( ) (4) / 35
16 A = {2, 3, 5, 7} = {7, 2, 5, 3} = {n n 10 } { = n n } n 4 17n n 2 247n = 0 () ( ) (4) / 35
17 2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) / 35
18 2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) / 35
19 2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) / 35
20 2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) / 35
21 2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) / 35
22 2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) / 35
23 2 B = {n 2 n 10 } = {2 2, 3 2, 5 2, 7 2 } = {4, 9, 25, 49} C = {m n m n 10 } = {2 2, 2 3, 2 5, 2 7, 3 2, 3 3, 3 5, 3 7, 5 2, 5 3, 5 5, 5 7, 7 2, 7 3, 7 5, 7 7} = {0, 1, 3, 5, 1, 0, 2, 4, 3, 2, 0, 2, 5, 4, 2, 0} = { 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5} ( ) (4) / 35
24 () N = () Z = () Q = () R = () C = () 2 N 3 N 3 Z 1 2 Z 1 2 Q 2 Q 2 R 1 + 2i R 1 + 2i C ( ) (4) / 35
25 () N = () Z = () Q = () R = () C = () 2 N 3 N 3 Z 1 2 Z 1 2 Q 2 Q 2 R 1 + 2i R 1 + 2i C ( ) (4) / 35
26 () N = () Z = () Q = () R = () C = () 2 N 3 N 3 Z 1 2 Z 1 2 Q 2 Q 2 R 1 + 2i R 1 + 2i C ( ) (4) / 35
27 () N = () Z = () Q = () R = () C = () 2 N 3 N 3 Z 1 2 Z 1 2 Q 2 Q 2 R 1 + 2i R 1 + 2i C ( ) (4) / 35
28 () N = () Z = () Q = () R = () C = () 2 N 3 N 3 Z 1 2 Z 1 2 Q 2 Q 2 R 1 + 2i R 1 + 2i C ( ) (4) / 35
29 {2, 3, 5, 7} ( ) (4) / 35
30 ( ) (4) / 35
31 A, B A B A B = {x x A x B} A = {a, b, c, d, e, f } B = {a, b, c, g, h} A B = {a, b, c} A d e f a b c g h B ( ) (4) / 35
32 A, B A B A B = {x x A x B} A = {a, b, c, d, e, f } B = {a, b, c, g, h} A B = {a, b, c, d, e, f, g, h} A d e f a b c g h B ( ) (4) / 35
33 A, B A B A B = {x x A x B} A = {a, b, c, d, e, f } B = {a, b, c, g, h} A B = {d, e, f } A d e f a b c g h B A BA \ B ( ) (4) / 35
34 1 { } 2 Φ φ ( ) (4) / 35
35 Constructive Solid Geometry Constructive Solid Geometry tree.png ( ) (4) / 35
36 ( ) (4) / 35
37 2 A = {a, b, c, d, e, f } B = {a, b, c, d, e, f, g, h, i} A B A a b c d e f B g h i () A B A B () ( ) (4) / 35
38 ( ) A B x A x B 2 A = {a, b, c, d, e, f } B = {a, b, c, d, e, f, g, h, i} A B A a b c d e f B g h i A B A B A B A B ( ) (4) / 35
39 N = Z = Q = R = C = N Z Z Q Q R R C ( ) (4) / 35
40 2 A B A B B A A = B B A A = B A and B ( ) (4) / 35
41 ( ) (4) / 35
42 1 1 A = {1, 2, 3} B = {2, 3, 4} A B ( 1 ) x {1, 2, 3} x {2, 3, 4} ( ) ( ) ( ) (4) / 35
43 1 1 A = {1, 2, 3} B = {2, 3, 4} A B ( 1 ) x {1, 2, 3} x {2, 3, 4} ( ) ( ) ( ) (4) / 35
44 1 1 A = {1, 2, 3} B = {2, 3, 4} A B ( 1 ) x {1, 2, 3} x {2, 3, 4} ( ) ( ) ( ) (4) / 35
45 1 ( ) 1 A = {1, 2, 3} B = {2, 3, 4} A B 1 A 1 B ( ) (4) / 35
46 2 2 A, B A B A B A, B A B A B A, B x A B x A B () ( ) (4) / 35
47 2 2 A, B A B A B A, B A B A B A, B x A B x A B () ( ) (4) / 35
48 2 2 A, B A B A B A, B A B A B A, B x A B x A B () ( ) (4) / 35
49 2 2 A, B A B A B A, B A B A B A, B x A B x A B () ( ) (4) / 35
50 2 ( ) 2 A, B A B A B A = {1, 2}, B = {2, 3} A B = {1, 2, 3} A B = {2} 1 A B 1 A B A B A B A, B x A B x A B () ( ) (4) / 35
51 2 ( ) 2 A, B A B A B A = {1, 2}, B = {2, 3} A B = {1, 2, 3} A B = {2} 1 A B 1 A B A B A B A, B x A B x A B () ( ) (4) / 35
52 2 ( ) 2 A, B A B A B A = {1, 2}, B = {2, 3} A B = {1, 2, 3} A B = {2} 1 A B 1 A B A B A B A, B x A B x A B () ( ) (4) / 35
53 ( ) (4) / 35
54 ( ) () ( ) (4) / 35
55 ( ) OK OK ( ) (4) / 35
56 ( ) (4) / 35
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