# Logica matematica

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• Publicado : 1 de junio de 2010

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taller de logica matematicas
1. p^q
p | q | p^q |
v | v | v |
v | f | f |
f | v | f |
f | f | f |

2. (p^q)^r
v | v | v | v | V |
v | v | v | f | F |
v | f | f | f | V |
v | f | f | f | F |
f | f | v | f | V |
f | f | v | f | F |
f | f | f | f | V |
f | f | f | f | F |

3. ~(p→~q)^(p^~)
v | v | f | f | F | v | f | f |
f | v | v | v | F | v | v | v |
f| f | v | f | F | f | f | f |
f | f | v | v | F | f | f | v |
2 1 r 3
4. (p ^ q) v (p v ~ q)
v | v | v | v | V | v | f |
v | f | f | v | V | v | v |
f | f | v | f | F | f | f |
f | f | f | v | F | v | v |
r
5. p ^ q ^ r
v | v | v | v | V |
v | v | v | f | F |
v | f | f | f | V |
v | f | f | f | F |
f |f | v | f | V |
f | f | v | f | F |
f | f | f | f | V |
f | f | f | f | F |
6. ~ ( p ^ ~ q ) ( p ^ ~ q )
v | f | f | f | V | f | f |
v | v | v | v | V | v | v |
f | f | f | f | F | f | f |
f | f | v | f | F | f | v |
1 r 2
7. ~ ~ ( ~ p ^ ~ q ) v ( p ^ ~ q )
v | v | v | v | V | f | f |
v | f | f | v | V | v | v |
f | f | v | f | F |f | f |
f | f | f | f | F | f | v |
1 r 2
8. p v q ^ r
v | v | v | v | V |
v | v | v | f | F |
v | v | f | v | V |
v | v | f | f | F |
f | v | v | v | V |
f | v | v | f | F |
f | f | f | f | V |
f | f | f | f | F |
1 r

9. ~ ( ~ p ^ ~ q ) ^ ( ~ p ^ ~ q )
v | f | f | f | F | f | f |
v | v | v | f | F | f | v |
f | f | f | f| V | f | f |
f | f | v | f | V | v | v |
1 r 2
10. p v q ^ ~ r
v | v | v | v | V |
v | v | v | f | F |
v | v | f | v | V |
v | v | f | f | F |
f | v | v | v | V |
f | v | v | f | F |
f | f | f | f | V |
f | f | f | f | F |
r

11. p ^ q → ~ r
v | v | v | v | F |
v | v | v | v | V |
v | f | f | v | F |v | f | f | v | V |
f | f | v | v | F |
f | f | v | v | V |
f | f | f | v | F |
f | f | f | v | V |
1 r

12. p ↔ ~ p
f |
f |
f |
f |

13. ~ ( p ^ q ) ^ ( p ^ ~ q )
v | f | f |
f | f | v |
v | f | f |
v | f | f |

14. ~ ~ p v ~ ~ q
v |
v |
v |
f |

15. p v q
v |
v |
v |
f |

16. p ↔ q v r
v | v |
v | v |
v | v |
v | v |f | v |
v | f |
f | v |
v | f |

17. [ ( ~ p v q ) v ( p ^ q ) ] → [ ( ~ p v q ) v ~ p ]
f | v | v | v | V | v | v | v | v |
v | v | f | f | F | f | v | v | v |
f | f | f | v | V | v | f | v | f |
f | f | f | v | V | v | v | v | v |

18. ( p v ~ q ) → ( ~ p → q )
v | v | v |
v | v | v |
f | v | f |
v | v | v |

19. ( p ↔ ~ q ) → ( ~ p → ~ q )
f | v | v |v | v | v |
v | v | f |
f | v | v |

20. ( ~p ^q )v (~ p v→ q )
f | v | v |
f | v | v |
v | v | v |
f | f | f |

21. ~ q v ~ p
f |
v |
v |
v |

(p→ q^ r)↔~ (~ q v r) v ~r
V | V | V | V | V | F | V | V | F | F | F |
V | V | V | F | F | F | V | V | V | V | V |
V | F | F | F | V | V | F | F | F | F | F |
V | F | F | F | F | F | F | V | V | V | V |
F | V | V| V | V | F | V | V | F | F | F |
F | V | V | F | F | F | V | V | V | V | V |
F | V | F | V | V | F | F | F | F | F | F |
F | V | F | F | F | F | F | V | V | V | V |

(~q ^ r )→ ~ (~ q v r) v ~r
F | F | V | V | V | V | F | V | F |
F | F | F | V | V | V | V | V | V |
V | V | V | F | F | F | F | F | F |
V | F | F | V | F | V | V | V | V |

( p →q ) ^ r → ~ ( p v r ) v ~ r
V | V| V | V | V | F | F | F | F | F | F |
V | V | V | F | F | V | F | V | V | V | V |
V | F | F | F | V | V | F | F | F | F | F |
V | F | F | F | F | V | F | V | V | V | V |
F | V | V | V | V | V | V | V | F | V | F |
F | V | V | F | F | V | V | V | V | V | V |
F | V | F | V | V | V | V | V | F | V | F |
F | V | F | F | F | V | V | V | V | V | V |

( p →q) ^( q→ r) →( p ^~ r)
V |...