離散数学第 1回論理 (1)：命題論理

1 (1) okamotoy@uecacjp 2012 4 10 2012 4 11 10:57 () (1) 2012 4 10 1 / 53

() (1) 2012 4 10 2 / 53

() 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) 2012 4 10 3 / 53

() (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) 2012 4 10 4 / 53

( ) 4 2 206 E-mailokamotoy@uecacjp Web (TA) ( ) 4 5 502 () E-mailkoizumi0836@gmailcom Webhttp://sitesgooglecom/site/yoshiookamotoy/discretemath 12 () (1) 2012 4 10 5 / 53

http://sitesgooglecom/site/yoshiookamotoy/discretemath 8 1 http://videofpuecacjp/ 1 () (1) 2012 4 10 6 / 53

(60 ) (30 ) (0 ) () () (1) 2012 4 10 7 / 53

30 () (1) 2012 4 10 8 / 53

6 4 1 20 120 100 100 90 () A4 1 () () (1) 2012 4 10 9 / 53

( ) () () () () (1) 2012 4 10 10 / 53

() 2007 Seymour Lipschutz 1995 2009 () 2010 () (1) 2012 4 10 11 / 53

( OK) () (1) 2012 4 10 12 / 53

1 2 3 4 5 6 () (1) 2012 4 10 13 / 53

() () 2004 http://www-groupsdcsst-andacuk/ history/pictdisplay/smullyanhtml () (1) 2012 4 10 14 / 53

55 2 18 19 () (1) 2012 4 10 15 / 53

1 2 3 4 5 6 () (1) 2012 4 10 16 / 53

() 4 Q () (1) 2012 4 10 17 / 53

2 2012 4 10 2012 2012 () (1) 2012 4 10 18 / 53

true false T F 1 0 T F () (1) 2012 4 10 19 / 53

1 2 3 4 5 6 () (1) 2012 4 10 20 / 53

() P = 4 Q = Q () (1) 2012 4 10 21 / 53

2 P = 4 Q = Q 4 Q () (1) 2012 4 10 22 / 53

() P P P P PP P P T F F T P = 4 P = 4 () (1) 2012 4 10 23 / 53

() 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) 2012 4 10 24 / 53

() 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) 2012 4 10 25 / 53

() 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) 2012 4 10 26 / 53

() 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) 2012 4 10 27 / 53

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) 2012 4 10 28 / 53

(P Q) ( P (R Q)) () () () P QP (Q + R) () (1) 2012 4 10 29 / 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 T F F T F T T F F F T T () (1) 2012 4 10 30 / 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) 2012 4 10 30 / 53

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) 2012 4 10 31 / 53

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) 2012 4 10 32 / 53

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) 2012 4 10 33 / 53

1 2 3 4 5 6 () (1) 2012 4 10 34 / 53

55 () 2 18 19 () (1) 2012 4 10 35 / 53

P = Q = P Q P (P Q) Q P (P Q)Q () (1) 2012 4 10 36 / 53

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) 2012 4 10 37 / 53

1 2 3 4 5 6 () (1) 2012 4 10 38 / 53

() 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) 2012 4 10 39 / 53

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) 2012 4 10 40 / 53

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) 2012 4 10 41 / 53

P P P P P P P T F T F T T () (1) 2012 4 10 42 / 53

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) 2012 4 10 43 / 53

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) 2012 4 10 44 / 53

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) 2012 4 10 45 / 53

(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) 2012 4 10 46 / 53

(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) 2012 4 10 47 / 53

() () (1) 2012 4 10 48 / 53

1 2 3 4 5 6 () (1) 2012 4 10 49 / 53

() (1) 2012 4 10 50 / 53

() () () 2008 2000 () (1) 2012 4 10 51 / 53

() OK OK () (1) 2012 4 10 52 / 53

1 2 3 4 5 6 () (1) 2012 4 10 53 / 53

離散数学 第 1回 論理 (1)：命題論理