離散数学 第 1回 論理 (1):命題論理

Size: px
Start display at page:

Download "離散数学 第 1回 論理 (1):命題論理"

Transcription

1 1 (1) :57 () (1) / 53

2 () (1) / 53

3 () 1 (1) (4 10 ) () (4 17 ) 2 (1) (4 24 ) 3 (2) (5 1 ) 4 (2) (5 8 ) 5 (3) (5 15 ) 6 (1) (5 22 ) 7 (2) (5 29 ) () (1) / 53

4 () (6 5 ) 8 (1) (6 12 ) 9 (2) (6 19 ) (6 26 ) 10 (3) (7 3 ) 11 (7 10 ) 12 (7 17 ) 13 (1) (7 24 ) 14 (2) (7 31 ) () (1) / 53

5 ( ) okamotoy@uecacjp Web (TA) ( ) () koizumi0836@gmailcom Webhttp://sitesgooglecom/site/yoshiookamotoy/discretemath 12 () (1) / 53

6 () (1) / 53

7 (60 ) (30 ) (0 ) () () (1) / 53

8 30 () (1) / 53

9 () A4 1 () () (1) / 53

10 ( ) () () () () (1) / 53

11 () 2007 Seymour Lipschutz () 2010 () (1) / 53

12 ( OK) () (1) / 53

13 () (1) / 53

14 () () history/pictdisplay/smullyanhtml () (1) / 53

15 () (1) / 53

16 () (1) / 53

17 () 4 Q () (1) / 53

18 () (1) / 53

19 () (1) / 53

20 () (1) / 53

21 () (1) / 53

22 () (1) / 53

23 () (1) / 53

24 () (1) / 53

25 () (1) / 53

26 () (1) / 53

27 () (1) / 53

28 () (1) / 53

29 () (1) / 53

30 () (1) / 53

31 () (1) / 53

32 true false T F 1 0 T F () (1) / 53

33 () (1) / 53

34 () P = 4 Q = Q () (1) / 53

35 2 P = 4 Q = Q 4 Q () (1) / 53

36 () P P P P PP P P T F F T P = 4 P = 4 () (1) / 53

37 () P Q P Q P Q AND P Q P Q T T T T F F F T F F F F P = 4 Q = Q P Q = 4 Q () (1) / 53

38 () P Q P Q P Q OR P Q P Q T T T T F T F T T F F F P = 4 Q = Q P Q = 4 Q () (1) / 53

39 () P Q P Q P Q P QP Q P Q P Q T T T T F F F T T F F T P = 4 Q = Q P Q = 4 Q () (1) / 53

40 () P Q P Q P Q P QP Q P Q P Q T T T T F F F T F F F T P = 4 Q = Q P Q = 4 Q () (1) / 53

41 P P P Q P Q P Q P Q P Q P Q P Q P Q P Q P Q P Q P Q P Q () (1) / 53

42 (P Q) ( P (R Q)) () () () P QP (Q + R) () (1) / 53

43 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F T F F T F T T F F F T T () (1) / 53

44 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F T F F T F T T F F F T T () (1) / 53

45 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F T F F T F T T F F F T T () (1) / 53

46 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F T F F T F T T F F F T T () (1) / 53

47 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F T F F T F T T F F F T T () (1) / 53

48 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F T F F T F T T F F F T T () (1) / 53

49 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F T F F T F T T F F F T T () (1) / 53

50 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F T F F T F T T F F F T T () (1) / 53

51 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F T F F T F T T F F F T T () (1) / 53

52 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F T F F T F T T F F F T T () (1) / 53

53 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F F T F F T T F T T F F F F T T T () (1) / 53

54 P Q (P Q) Q P Q P Q Q P Q Q (P Q) Q P Q Q P Q P Q Q (P Q) Q T T T F F T F F T T F T T F F F F T T T () (1) / 53

55 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

56 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

57 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

58 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

59 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

60 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

61 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

62 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

63 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

64 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

65 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

66 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

67 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

68 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

69 1 P, Q (P (Q P)) P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

70 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

71 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

72 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

73 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

74 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

75 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

76 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

77 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

78 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

79 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

80 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

81 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

82 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

83 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

84 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

85 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

86 2 P, Q, R (P R) ((P Q) (R Q)) P Q R P Q R Q P R (P Q) (R Q) (P R) ((P Q) (R Q)) T T T T T T T T T T F T F F T F T F T F F T F F T F F F T F T F F T T F T T T T F T F F F T F F F F T T F T T T F F F T T T T T () (1) / 53

87 1 1 () P Q P Q P P (Q P) (P (Q P)) T T F T T F T F F F F T F T T T F T F F T T F T () (1) / 53

88 () (1) / 53

89 55 () () (1) / 53

90 P = Q = P Q P (P Q) Q P (P Q)Q () (1) / 53

91 P Q P Q (P Q) P (P Q) T T T F F T F F T T F T F T F F F F T F P (P Q) Q () (1) / 53

92 () (1) / 53

93 () P (Q P) P Q Q P P (Q P) T T T T T F T T F T F T F F T T () (1) / 53

94 P, Q (P Q) ( P Q) P Q P P Q P Q (P Q) ( P Q) T T F T T T T F F F F T F T T T T T F F T T T T () (1) / 53

95 P, Q (P Q) ((P Q) (Q P)) P Q P Q P Q Q P (P Q) (Q P) (P Q) ((P Q) (Q P)) T T T T T T T T F F F T F T F T F T F F T F F T T T T T () (1) / 53

96 P P P P P P P T F T F T T () (1) / 53

97 P, Q 2 ( (P Q)) ( P Q) ( (P Q)) ( P Q) P Q P Q P Q P Q (P Q) ( (P Q)) ( P Q) T T F F F T F T T F F T F T F T F T T F F T F T F F T T T F T T P Q P Q P Q P Q (P Q) ( (P Q)) ( P Q) T T F F F T F T T F F T T F T T F T T F T F T T F F T T T F T T () (1) / 53

98 P, Q (P (P Q)) Q P Q P Q P (P Q) (P (P Q)) Q T T T T T T F F F T F T T F T F F T F T () (1) / 53

99 P, Q (P Q) ( Q P) P Q P Q Q P Q P (P Q) ( Q P) T T T F F T T T F F T F F T F T T F T T T F F T T T T T () (1) / 53

100 (1) (P P) P (P P) P (P Q) (Q P) (P Q) (Q P) ((P Q) R) (P (Q R)) ((P Q) P) P ((P Q) P) P P ( P) ((P Q) R) (P (Q R)) () (1) / 53

101 (2) ((P Q) R) ((P R) (Q R)) ((P Q) R) ((P R) (Q R)) (P T) P (P F) F (P F) P (P T) T ((P Q) (P R)) (P (Q R)) ((P Q) (Q R)) (P R) () (1) / 53

102 () () (1) / 53

103 () (1) / 53

104 () (1) / 53

105 () () () () (1) / 53

106 () OK OK () (1) / 53

107 () (1) / 53

=

= 2. 2.1 2.2 kuri@ice.uec.ac.jp ( 2007/10/30/16:46) 1 . 1. 1 + 2 = 5. 2. 180. 3. 3 3. 4.. 5.. 2 2.1 1.,,,,. 2., ( ) ( ).,,,, 3.,. 4.,,,. 3 1.,. 1. 1 + 2 = 5. (, ) 2. 180. (, ) 3. 3, 3. (, ) 4.. (, ) 5..

More information

レイアウト 1

レイアウト 1 1 1 3 5 25 41 51 57 109 2 4 Q1 A. 93% 62% 41% 6 7 8 Q1-(1) Q2 A. 24% 13% 52% Q3 Q3 A. 68% 64 Q3-(2) Q3-(1) 9 10 A. Q3-(1) 11 A. Q3-(2) 12 A. 64% Q4 A. 47% 47% Q5 QQ A. Q Q A. 13 QQ A. 14 Q5-(1) A. Q6

More information

10_11p01(Ł\”ƒ)

10_11p01(Ł\”ƒ) q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q

More information

2 1 2 3 27 2 6 2 5 19 50 1 2

2 1 2 3 27 2 6 2 5 19 50 1 2 1 2 1 2 3 27 2 6 2 5 19 50 1 2 2 17 1 5 6 5 6 3 5 5 20 5 5 5 4 1 5 18 18 6 6 7 8 TA 1 2 9 36 36 19 36 1 2 3 4 9 5 10 10 11 2 27 12 17 13 6 30 16 15 14 15 16 17 18 19 28 34 20 50 50 5 6 3 21 40 1 22 23

More information

日経テレコン料金表(2016年4月)

日経テレコン料金表(2016年4月) 1 2 3 4 8,000 15,000 22,000 29,000 5 6 7 8 36,000 42,000 48,000 54,000 9 10 20 30 60,000 66,000 126,000 166,000 50 100 246,000 396,000 1 25 8,000 7,000 620 2150 6,000 4,000 51100 101200 3,000 1,000 201

More information

73 p.1 22 16 2004p.152

73 p.1 22 16 2004p.152 1987 p.80 72 73 p.1 22 16 2004p.152 281895 1930 1931 12 28 1930 10 27 12 134 74 75 10 27 47.6 1910 1925 10 10 76 10 11 12 139 p.287 p.10 11 pp.3-4 1917 p.284 77 78 10 13 10 p.6 1936 79 15 15 30 80 pp.499-501

More information

2 2 3 4 5 5 2 7 3 4 6 1 3 4 7 4 2 2 2 4 2 3 3 4 5 1932 A p. 40. 1893 A p. 224, p. 226. 1893 B pp. 1 2. p. 3.

2 2 3 4 5 5 2 7 3 4 6 1 3 4 7 4 2 2 2 4 2 3 3 4 5 1932 A p. 40. 1893 A p. 224, p. 226. 1893 B pp. 1 2. p. 3. 1 73 72 1 1844 11 9 1844 12 18 5 1916 1 11 72 1 73 2 1862 3 1870 2 1862 6 1873 1 3 4 3 4 7 2 3 4 5 3 5 4 2007 p. 117. 2 2 3 4 5 5 2 7 3 4 6 1 3 4 7 4 2 2 2 4 2 3 3 4 5 1932 A p. 40. 1893 A p. 224, p. 226.

More information

29 2011 3 4 1 19 5 2 21 6 21 2 21 7 2 23 21 8 21 1 20 21 1 22 20 p.61 21 1 21 21 1 23

29 2011 3 4 1 19 5 2 21 6 21 2 21 7 2 23 21 8 21 1 20 21 1 22 20 p.61 21 1 21 21 1 23 29 2011 3 pp.55 86 19 1886 2 13 1 1 21 1888 1 13 2 3,500 3 5 5 50 4 1959 6 p.241 21 1 13 2 p.14 1988 p.2 21 1 15 29 2011 3 4 1 19 5 2 21 6 21 2 21 7 2 23 21 8 21 1 20 21 1 22 20 p.61 21 1 21 21 1 23 1

More information

308 ( ) p.121

308 ( ) p.121 307 1944 1 1920 1995 2 3 4 5 308 ( ) p.121 309 10 12 310 6 7 ( ) ( ) ( ) 50 311 p.120 p.142 ( ) ( ) p.117 p.124 p.118 312 8 p.125 313 p.121 p.122 p.126 p.128 p.156 p.119 p.122 314 p.153 9 315 p.142 p.153

More information

122011pp.139174 18501933

122011pp.139174 18501933 122011pp.139174 18501933 122011 1850 3 187912 3 1850 8 1933 84 4 1871 12 1879 5 2 1 9 15 1 1 5 3 3 3 6 19 9 9 6 28 7 7 4 1140 9 4 3 5750 58 4 3 1 57 2 122011 3 4 134,500,000 4,020,000 11,600,000 5 2 678.00m

More information

Microsoft Word - 映画『東京裁判』を観て.doc

Microsoft Word - 映画『東京裁判』を観て.doc 1 2 3 4 5 6 7 1 2008. 2 2010, 3 2010. p.1 4 2008 p.202 5 2008. p.228 6 2011. 7 / 2008. pp.3-4 1 8 1 9 10 11 8 2008, p.7 9 2011. p.41 10.51 11 2009. p. 2 12 13 14 12 2008. p.4 13 2008, p.7-8 14 2008. p.126

More information

() L () 20 1

() L () 20 1 () 25 1 10 1 0 0 0 1 2 3 4 5 6 2 3 4 9308510 4432193 L () 20 1 PP 200,000 P13P14 3 0123456 12345 1234561 2 4 5 6 25 1 10 7 1 8 10 / L 10 9 10 11 () ( ) TEL 23 12 7 38 13 14 15 16 17 18 L 19 20 1000123456

More information

戦後の補欠選挙

戦後の補欠選挙 1 2 11 3 4, 1968, p.429., pp.140-141. 76 2005.12 20 14 5 2110 25 6 22 7 25 8 4919 9 22 10 11 12 13 58154 14 15 1447 79 2042 21 79 2243 25100 113 2211 71 113 113 29 p.85 2005.12 77 16 29 12 10 10 17 18

More information

untitled

untitled 186 17 100160250 1 10.1 55 2 18.5 6.9 100 38 17 3.2 17 8.4 45 3.9 53 1.6 22 7.3 100 2.3 31 3.4 47 OR OR 3 1.20.76 63.4 2.16 4 38,937101,118 17 17 17 5 1,765 1,424 854 794 108 839 628 173 389 339 57 6 18613

More information

untitled

untitled 1. 3 14 2. 1 12 9 7.1 3. 5 10 17 8 5500 4. 6 11 5. 1 12 101977 1 21 45.31982.9.4 79.71996 / 1997 89.21983 41.01902 6. 7 5 10 2004 30 16.8 37.5 3.3 2004 10.0 7.5 37.0 2004 8. 2 7 9. 6 11 46 37 25 55 10.

More information

夏目小兵衛直克

夏目小兵衛直克 39(1906)1222 14(1817) 3(1832)1514(1843) 2628 6 (1853) (1854)3727 3(1856) 1 / 13 5(1858)6(1859) 5(1853) () () () () () () 3(1867)29 504111( 2 / 13 )98 23 18 2(1869)310283 100 50() 58 226 3313200982 5033

More information

-1-

-1- -1- -2- -3-1 8 6% 2 4 6 8 1 48 63 43 6 55 38 78 58 2 88 67 11 22 78 1 56 22 89 47 34 36 32 38 4 34 26 7 -4- 18-5- 3 25 28 (6.%) (6.%) (.9%) 2 15 18 158 1 (3.8%) (56.4%) 5 2 137 27 8 1 68 119 26 71 28 65

More information

( )

( ) Web Web 1 3 1 21 11 22 23 24 3 2 3 4 5 1 1 11 22 9 2 3 15 11 22 2 11 21 4 5 ( ) 102 ( ) 1 ( 1 2001 Web 1 5 4 1 1 - 7 - [] - 7 10 11 12 12 1 10 1 12 - [] 1 1 2 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 3 1 47

More information

nenkin.PDF

nenkin.PDF 1 31 1 WEB 10 3,544 429 13 10 22 11 7 WEB 1 2 41.0 15 80.0 20 46.7% 1000 55.8 1000 34.4 21 18.2 1000 23 25 41.0 49.2 29 90.6 42.7 33 56.4% 79.2% 67.4 51.7 37 39 83.7 1 91.0 93.6 9 2 3 1000 96.3 300 1000

More information

離散数学 第 2回 集合と論理 (2):集合と論理の対応

離散数学 第 2回  集合と論理 (2):集合と論理の対応 2 (2) okamotoy@uec.ac.jp 2015 4 17 2015 4 15 14:10 ( ) (2) 2015 4 17 1 / 40 ( ) 1 (1) (4 10 ) 2 (2) (4 17 ) 3 (3) (4 24 ) 4 (1) (5 1 ) 5 (2) (5 8 ) 6 (4) (5 15 ) 7 (3) (5 22 ) 8 (1) (5 29 ) 9 (2) (6 5

More information

離散数学 第 4回 集合の記法 (1):外延的記法と内包的記法

離散数学 第 4回  集合の記法 (1):外延的記法と内包的記法 4 (1) okamotoy@uec.ac.jp 2014 5 13 2014 5 12 09:28 ( ) (4) 2014 5 13 1 / 35 () 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

More information

1

1 1 1 2 3 4 5 6 7 8 9 10 11 Q7 3 0.0 10.0 20.0 30.0 40.0 50.0 18-29 30-39 40-49 12 Q8 Q7 0 20 40 60 23 23 13 14 15 16 Q10 3 0.0 20.0 40.0 60.0 80.0 18-29 30-39 40-49 17 18 Q12 3 0.0 10.0 20.0 30.0 40.0 18-29

More information

Ⅱ 本編 19 1 23 1-1 - 16 - - 17-1-3 1-2 - 18 - - 19 - - 20 - - 21 - - 22 - 3 10 60 1,000 3,000-24 - 23.9% 19.2% 16.6% 37.4% 32.3% - 25 - 300500 27.6% 500700 21.0% 300 20.2% 7001,000 17.9% 1,000 13.3% 2-1-6-26

More information

離散数理工学 第 2回 数え上げの基礎:漸化式の立て方

離散数理工学 第 2回  数え上げの基礎:漸化式の立て方 2 okamotoy@uec.ac.jp 2015 10 20 2015 10 18 15:29 ( ) (2) 2015 10 20 1 / 45 ( ) 1 (10/6) ( ) (10/13) 2 (10/20) 3 ( ) (10/27) (11/3) 4 ( ) (11/10) 5 (11/17) 6 (11/24) 7 (12/1) 8 (12/8) ( ) (2) 2015 10 20

More information

経済論集 46‐2(よこ)(P)☆/2.三崎

経済論集 46‐2(よこ)(P)☆/2.三崎 1 2 1869 11 17 5 10 1 3 1914 5 15 5 1872 9 12 3 1870 1 26 14 1881 11 11 12 6 11 1878 5 9 13 1880 6 17 1 15 1882 1 2 3 11 1828 2 26 24 1891 4 22 2 1849 12 1 3 1856 pp 20 21. 1971 p.429. 1973 1, pp.440 444.

More information

2 3 5 5 5 5 6 6 7 7 8 10 10 10 10 11 11 12 12 13 16 16 16 16 17 19 21 21 22 5

2 3 5 5 5 5 6 6 7 7 8 10 10 10 10 11 11 12 12 13 16 16 16 16 17 19 21 21 22 5 1D000425-2 1 2 3 5 5 5 5 6 6 7 7 8 10 10 10 10 11 11 12 12 13 16 16 16 16 17 19 21 21 22 5 3 29 29 29 30 31 31 32 35 35 35 36 41 41 41 46 48 48 48 52 57 4 700 13 1988 4 5 4 5 21 1 1 3 4 5 6 21 10 1888

More information

株主通信:第16期 中間報告書

株主通信:第16期 中間報告書 9 1 20,000 15,000 10,000 5,000 2007/4 2008/4 2009/4 2010/4 2011/4 2012/4 2013/4 01 02 2 3 03 04 4 05 06 5 133,362 206,945 344,360 363,936 67,583 128,114 819 18,583 412,477 846,445 164,935 422,265 1,433,645

More information

福岡大学人文論叢47-3

福岡大学人文論叢47-3 679 pp. 1 680 2 681 pp. 3 682 4 683 5 684 pp. 6 685 7 686 8 687 9 688 pp. b 10 689 11 690 12 691 13 692 pp. 14 693 15 694 a b 16 695 a b 17 696 a 18 697 B 19 698 A B B B A B B A A 20 699 pp. 21 700 pp.

More information

P15 P211 1 P1 P4 P2 P3 P4 P17

P15 P211 1 P1 P4 P2 P3 P4 P17 P15 P211 1 P1 P4 P2 P3 P4 P17 P3 P4 P7 P8 P9 2 1 Q A P17 P17 1 2 3 4 3 5 6 7 8 2 P17 Q A P17 4 1 2 3 4 2 P17 P4 P12 P17 P4 5 5 6 7 8 2 P4 P4 6 1 2 3 4 3 P17 P10 P17 7 5 6 7 8 4 0120-096-991 P17 8 1 2 3

More information

,255 7, ,355 4,452 3,420 3,736 8,206 4, , ,992 6, ,646 4,

,255 7, ,355 4,452 3,420 3,736 8,206 4, , ,992 6, ,646 4, 30 8 IT 28 1,260 3 1 11. 1101. 1102. 1103. 1 3 1,368.3 3 1,109.8 p.5,p.7 2 9,646 4,291 14.5% 10,p.11 3 3,521 8 p.13 45-49 40-44 50-54 019 5 3 1 2,891 3 6 1 3 95 1 1101 1102 1103 1101 1102 1103 1 6,255

More information

離散数理工学 第 2回 数え上げの基礎:漸化式の立て方

離散数理工学 第 2回  数え上げの基礎:漸化式の立て方 2 okamotoy@uec.ac.jp 2014 10 21 2014 10 29 10:48 ( ) (2) 2014 10 21 1 / 44 ( ) 1 (10/7) ( ) (10/14) 2 (10/21) 3 ( ) (10/28) 4 ( ) (11/4) 5 (11/11) 6 (11/18) 7 (11/25) ( ) (2) 2014 10 21 2 / 44 ( ) 8 (12/2)

More information

(1) (2)

(1) (2) 1998 2000 (1) (2) (3) 1997 11 25 1998 6 17 1997 89 25 (4) (5) 25 25 25 1 1993 (6) 1998 12 8 2 2000 6 (7) (8) 1980 1990 (9) (10) (11) 1 8/10 1986 1989 1986 1987 86 (12) (13) 2 1989 1989 3 (14) 1989 12 10

More information

untitled

untitled ...1...3 -... 3 -... 3...5 -... 5 -... 5 -... 6 -... 7 -... 7 -... 7 -... 10 -... 17 -... 17 -... 18 -... 20 -... 21 1 TEL 2 3 4 ) ) 5 6 7 8 9 10 11 () (4) () (4) () () 730-0042730-8586 730-0042 730-0042730-8586

More information

untitled

untitled P04 P23 P21 01 CONTENTS P0305 P28 30 P28 1 2 3 4 5 P07 P09 P13 P15 P19 P30 6 P21 7 8 P22 P25 02 03 04 05 P04 P07P28 P29 06 1 2 3 4 1 07 5-1 -2 6 7-1 -2 8 08 1 2 3 4 2 1 09 5-1 -2 6 7-1 -2 8 10 1 2 3 4

More information

1 P2 P P3P4 P5P8 P9P10 P11 P12

1 P2 P P3P4 P5P8 P9P10 P11 P12 1 P2 P14 2 3 4 5 1 P3P4 P5P8 P9P10 P11 P12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 & 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1! 3 2 3! 4 4 3 5 6 I 7 8 P7 P7I P5 9 P5! 10 4!! 11 5 03-5220-8520

More information

本組よこ/根間:文11-029_P377‐408

本組よこ/根間:文11-029_P377‐408 377 378 a b c d 379 p M NH p 380 p 381 a pp b T 382 c S pp p 383 p M M 384 a M b M 385 c M d M e M 386 a M b M a M 387 b M 388 p 389 a b c 390 391 a S H p p b S p 392 a T 393 b S p c S 394 A a b c d 395

More information

2009/02/ /03/ /03/ /06/16 21

2009/02/ /03/ /03/ /06/16 21 2009 6 2009/02/25 3 3 2009/03/03 3 10 2009/03/10 6 16 2009/06/16 21 ... 1 1... 3 1-1... 3 1-2... 3 1-3... 3 1-4... 4 1-5... 6 2... 7 2-1 ( )... 7 3... 13 4... 16 4-1... 16 4-2... 17 4-3... 18 5... 19 5-1...

More information

MultiWriter 5650C 活用マニュアル

MultiWriter 5650C 活用マニュアル 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 11 1 2 3 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 1 2 3 a b c 30 31 32 C *1 *2 *2 33 2 2 2 2 2 2 2 2 2 34 *1 *2 ± *1 C C 35 36 37 38 39 40 OK 1 2 3 4

More information

21 1 2 1 2

21 1 2 1 2 21 1 2 1 2 1 2 3 ( ) 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 210 0.0 0.0 22 23 25 27 28 29 30 31 32 33 34 35 36 74 pp.4362003.10 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 141224 14 48 10

More information

P.1P.3 P.4P.7 P.8P.12 P.13P.25 P.26P.32 P.33

P.1P.3 P.4P.7 P.8P.12 P.13P.25 P.26P.32 P.33 : : P.1P.3 P.4P.7 P.8P.12 P.13P.25 P.26P.32 P.33 27 26 10 26 10 25 10 0.7% 331 % 26 10 25 10 287,018 280,446 6,572 30,236 32,708 2,472 317,254 313,154 4,100 172,724 168,173 4,551 6,420 6,579 159 179,144

More information

pp. 2123 pp. 6364 pp. 147149 p. 141 pp. 3942 pp. 122123 p. 195

pp. 2123 pp. 6364 pp. 147149 p. 141 pp. 3942 pp. 122123 p. 195 pp. 5556 pp. 2123 pp. 6364 pp. 147149 p. 141 pp. 3942 pp. 122123 p. 195 pp. 9091 J-FIC p. 31 JFIC p. 60 pp. 5354 pp. 1013 p. 142 p. 141 pp. 143144 pp. 1521 pp. 8182 p. 96 p. 140 p. 140 p. 142 p. 41 p.

More information

報告書

報告書 1 2 3 4 5 6 7 or 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2.65 2.45 2.31 2.30 2.29 1.95 1.79 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 60 55 60 75 25 23 6064 65 60 1015

More information

納税者番号制度の導入と金融所得課税

納税者番号制度の導入と金融所得課税 () 1 2 () 16 4 2 () 3 1 ( 63 ) 2 3 1 () 54 37 4 5 ( 55 ) 6 () 7 55 3 ( 55 8 ) () 58 60 3 61 4 5 6 300 300 62 9 15 7 2 63 ( 1 ) 8 4 4 11 2 9 15 6 16 6 20 9 17 17 10 8 9 10 3 11 62 12 26 2 10 30 38 () 46

More information

1% 51% 4% 13% 31% 152 50 47 36 32 21 20 20 16 14 7 3 1

1% 51% 4% 13% 31% 152 50 47 36 32 21 20 20 16 14 7 3 1 1% 13 13 19 20 1% 80 9% 70 41% 60 34% 30 3% 40 5% 50 6% 51% 2% 47% 3% 1% 14% 10% 23% 49% 1% 51% 4% 13% 31% 152 50 47 36 32 21 20 20 16 14 7 3 1 102 228 OK 228 46 42 17 10 8 6 5 1 14% 25% 1% 3% 7% 27% 23%

More information

untitled

untitled 7/67/1073,42911 15,020158,393 7/127/184,6674,913 2927 71.3 894 21.8 287 7.0 n=4108) 132 3.2 62 1.5 934 22.7 786 19.1 629 15.3 801 19.5 407 9.9 357 8.7 (n=4108) 35 35 30 25 20 15 10 153 3.7 1 0.02 23 0.6

More information

untitled

untitled 2003 6 9 244 2 3 11 46 71011 10 11 1 15 7 17 87 (http://www.pficenter.jp/shiryou/link02.html/) ) 2 244 3 244 4 2 180 3 3 4 3 4 4 , 10 10 5 10 (1)(2)(3) (2),, 6 ,,,,,,,,,,, 7 ,,,,,,,,, NPO,,,,,,,,,,,,,,,,,,

More information

81 34 6 5 6 6 5 5 6 1 5 2 6 176 414

81 34 6 5 6 6 5 5 6 1 5 2 6 176 414 5 6 5 6 5 6 5 4 4 6 5 5 5 413 175 81 34 6 5 6 6 5 5 6 1 5 2 6 176 414 1 5 5 12 3 4 5 1 1 2 3 2 1 415 177 81 34 2 3 4 5 3 1 2 4 5 1 1 1 4 178 416 65,000 35,000 6,000 2 4 417 179 81 34 4 10,000 5,000 750

More information

定職につけない若者たち(4班)

定職につけない若者たち(4班) 4 01641 01682 01716 01718 01777 1 1. 1 2. 1 3. 2 4. 4 5. 5 6. 6 7. 7 8. 8 9. 12 10. 13 11. 15 12. 17 13. 18 19 2 1. 2. 60 14 63 2 3 12 13 5 14 5.4 14 359 13 19 28 3 2 19772001 3. 82 50 2002 209 4 4 1982

More information

untitled

untitled 16 4 1 17 1 50 -1- -2- -3- -4- -5- -6- -7- 1 2-8- -9- -10- -11- Web -12- (1) (2)(1) (3) (4) (1)()(2) (3)(4) -13- -14- -15- -16- -17- -18- -19- -20- -21- -22- -23- (2)(1) (3) -24- -25- -26- -27- -28- -29-

More information

A P18 P11 P P1 P4 P17 P3 P4 1

A P18 P11 P P1 P4 P17 P3 P4 1 A P18 P11 P P1 P4 P17 P3 P4 1 P3 P4 P7 P8 P9 1 Q A 1 3 4 P17 P17 3 6 7 8 P17 P13 Q A P17 4 1 3 4 P17 P14 P4 P13 P17 P4 6 7 8 P4 P4 6 1 3 4 3 P17 P17 7 6 7 8 4 010-096-991 P17 8 1 3 4 P17 P17 Q A 9 6 7

More information

<83588389837593C195CA8D868151303888E48AC0975420976C2E706466>

<83588389837593C195CA8D868151303888E48AC0975420976C2E706466> 2013 pp. 99-119 1920 3 5 (1) (2) (1) 2001 19209 2 5 4000 3 12 130 75 25 (2) 23 1975 2 17 2 3 1917 19221989 81995 62 84 (3) (4) (5) (6) (7) (8) (narrative) (9) (10) 45 1987 61 70 (4) 2011 (5) 1985 205 235

More information

(1)

(1) ~ ~ NO YES ~ ( NO YES ) YES NO NO YES ~ ( NO YES ) YES NO 1 1 NO 2 NO 2YES YES 1 (1) 25 26 2 3 () () () () 4 () () 5 6 () 7 () 8 9 1-3-1 10 3 11 12 ~1. (1) () () (2) (3) () (4) () () (5) (6) (7) (1) (2)

More information