Demostraciones Lógica Matemática Discreta
XjhonALPráctica o problema26 de Abril de 2019
7.668 Palabras (31 Páginas)283 Visitas
[pic 2]
Demostraciones | G2 |
[pic 3]
E.A.P Ingeniería de Sistemas | Matemática Discreta |
A) DEMOSTRAR: [pic 4]
[pic 5]
[pic 6]
DE [pic 8][pic 9][pic 10][pic 7]
1 Premisa 1[pic 11]
2 Premisa 2[pic 12]
3 DE [pic 14][pic 15][pic 13]
3.1 Premisa[pic 17][pic 16]
3.2 DE [pic 19][pic 20][pic 18]
3.2.1 ¬P Premisa[pic 21]
3.2.2 Q ¬Q –I, 3.1, 2[pic 22][pic 23]
3.3 ¬ –E, 3.2[pic 24]
4 Q→P Definicion→3[pic 25]
5 P ∨-E 4.1
Ó[pic 26]
DE [pic 28][pic 29][pic 30][pic 27]
1 Premisa 1[pic 31]
2 Premisa 2[pic 33][pic 32]
3 DE [pic 35][pic 36][pic 34]
3.1 ¬P
3.2 ¬P∨Q
3.3 P→Q
3.4 Q [pic 37]
3.5 Q ¬Q [pic 39][pic 38]
4 P
B) DEMOSTRAR:
[pic 40]
[pic 41]
DE [pic 43][pic 44][pic 45][pic 42]
1 A →B Premisa1
2 B → (C D) Premisa2 [pic 46]
3 (C E) →F Premisa3 [pic 47]
4 A E Premisa4 [pic 48]
5 A Λ – E, 4
6 E Λ – E, 4
7 B → -E, 1, 5
8 C D → -E, 2, 7[pic 49]
9 C Λ –E, 8
10 C E Λ -I, 9,6[pic 51][pic 50]
11 F
C) DEMOSTRAR:
[pic 52]
[pic 53]
[pic 54]
DE [pic 56][pic 57][pic 55]
1 P Λ Q Premisa
2 P→R Premisa
3 P Λ-E ,1
4 Q Λ-E,1
5 R →-E 3,2 [pic 58][pic 59]
6 DE [pic 61][pic 60]
6.1 Q Premisa [pic 62]
6.2 R
7 Q→R Definición →6[pic 63]
8 R Λ (Q→R )
D) DEMOSTRAR:
[pic 64]
[pic 65]
DE [pic 67][pic 68][pic 66]
1 P ∨ Q Premisa 1
2 P→R Premisa 2
3 ¬R Premisa 3 [pic 69]
4 DE [pic 71][pic 70]
4.1 ¬Q Premisa
4.2 ¬Q → P def, 1
4.3 P [pic 72]
4.4 R [pic 73][pic 74]
5 Q ¬ -E, 4
Ó
E) DEMOSTRAR:
[pic 75]
[pic 76]
[pic 77]
DE [pic 79][pic 80][pic 78]
1 P ∨ Q Premisa 1
2 P→R Premisa 2
3 ¬R Premisa 3
4 DE [pic 82][pic 83][pic 81]
4.1 ¬Q Premisa
4.2 R ∨-E 1,2[pic 84]
4.3 R Λ¬R Λ-I 4.2,3[pic 85]
5 Q ¬ -E, 4
...