Discretas 1

República Bolivariana de Venezuela
Ministerio del Poder Popular para la Educación Superior
Universidad Fermín Toro

Integrante:
Rafael Ramírez
18263403

Ejercicios propuestos
5.a
( | P |^ | ~q | ) | ^ | r |
| 1 | | 0 | | | 0 |
| | 0 | | ^ | | 0 |
| | | | | 0 | |

5.b
( | p | | q | ) | v | ( | ~q | | r | ) |
| 1 | | 1 | | | | 0 | | 1 | |
| | 1| | | | | | 1 | | |
| | | | | 0 | | | | | |

5.c
( | P | ^ | Q | ) | ↔ | [ | P | V | (q | ^ | ~r) | ] |
| 1 | | 1 | | | | 1 | | 1 | | 1 | |
| | 1 | | | | |1 | | | 1 | | |
| | 1 | | | 1 | | | 1 | | | | |

5.d
( | P | ↔ | ~r | ) | ↔ | ( | Q | ↔ | P | V | R | ) |
| 1 | | 1 | | | | 1 | | 1 | | 0 | |
| | 1 | | | | | |1 | | | 0 | |
| | 1 | | | | | | | | 1 | | |
| | | | | 1 | | | | | | | |

6.
[ | ( | ~p | → | Q | ) | ^ | P | ] | → | ~q |
| | 1 | | 1 | | | 0 | | | 0 || | | 1 | | | | 0 | | | |
| | | | | | 1 | | | | 0 |
| | | | | | | | | 0 | |
VL(P)=0; VL(Q)=1.
7
VL(M)=1 ;
VL(R)=0;
VL(T)=0;

8
VL(p)=1 ;
VL(q)=0;
VL(r)=1;9
VL(p)=1 ;
VL(q)=0;
VL(r)=1;
13.

(P | → | Q | V | R) | ↔ | [~R | → | (P | → | q) | ] |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | |
1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | |1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | |
1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | |
0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | |
0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | |
0 |1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | |
0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | |

Si es tautología debido a que su columna principal o resultado esta compuesta solo por valores positivos(P | → | Q) | ^ | (R | → | q) | ↔ | (P | V | R | → | q) |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
1 | 0 | 0 | 0 | 1 | 0 |...