Soporte Tecnico

EJERCICIOS
A. Usando tablas de verdad demostrar lo siguiente
Nota: Recordar que V significa verdadero, F es falso, ~ es NOT

1. ~(~p) = p
p | ~p | ~(~p) |
V | | |
F | | |

2. p and ~(p) = Falso
p | ~p | p and ~p |
V | | |
F | | |

3. p or ~(p) = Verdadero
p | ~p | P or ~p |
V | | |
F | | |

4. p or V = Verdadero
p | | p or V |
V | V | |
F | V ||

5. p and Verdadero = p
p | | p and V |
V | V | |
F | V | |

6. p or Falso = p
p | | p or F |
V | F | |
F | F | |

7. p and Falso = Falso
p | | |
V | | |
F | | |

8. p and ( p or q) = p
p | q | p or q | p and( p or q) |
V | V | | |
V | F | | |
F | V | | |
F | F | | |

9. p or (p and q) = p

p | q | p and q | p or ( p and q) |
V |V | | |
V | F | | |
F | V | | |
F | F | | |

10. ~(p and q) = ~(p) or ~(q)
p | q | p and q | ~(p and q) | ~(p) | ~(q) | ~(p) or ~(q) |
V | V | | | | | |
V | F | | | | | |
F | V | | | | | |
F | F | | | | | |

11. ~(p or q) = ~(p) and ~(q)
p | q | p or q | ~ (p or q) | ~(p) | ~(q) | ~(p) and ~(q) |
V | V | | | | | |
V | F | | | | | |F | V | | | | | |
F | F | | | | | |

12. (p and q) and r = p and (q and r)

p | q | r | p and q | (p and q) and r | (q and r) | p and (q and r) |
V | V | V | | | | |
V | V | F | | | | |
V | F | V | | | | |
V | F | F | | | | |
F | V | V | | | | |
F | V | F | | | | |
F | F | V | | | | |
F | F | F | | | | |

13. (p or q) or r = p or(q or r)
p | q | r | p or q | (p and q) or r | (q or r) | p or (q or r) |
V | V | V | | | | |
V | V | F | | | | |
V | F | V | | | | |
V | F | F | | | | |
F | V | V | | | | |
F | V | F | | | | |
F | F | V | | | | |
F | F | F | | | | |

14. (p ↔ q) ↔r = p ↔ (q ↔r)
p | q | r | p ↔ q | (p ↔ q) ↔ r | (q ↔ r) | p ↔ (q ↔ r) |
V | V | V | | || |
V | V | F | | | | |
V | F | V | | | | |
V | F | F | | | | |
F | V | V | | | | |
F | V | F | | | | |
F | F | V | | | | |
F | F | F | | | | |

15. p and (q or r) = (p and q) or (p and r)
p | q | r | p or q | p and (q or r) | (p and q) | (p and r) | (p and) or (p and r) |
V | V | V | | | | | |
V | V | F | | | | | |
V | F | V | | || | |
V | F | F | | | | | |
F | V | V | | | | | |
F | V | F | | | | | |
F | F | V | | | | | |
F | F | F | | | | | |

16. p or (q and r) = (p or q) and (p or r)
p | q | r | q and r | p or (q and r) | (p or q) | (p or r) | (p and) and (p and r) |
V | V | V | | | | | |
V | V | F | | | | | |
V | F | V | | | | | |
V | F | F | | | || |
F | V | V | | | | | |
F | V | F | | | | | |
F | F | V | | | | | |
F | F | F | | | | | |

17. ~p or q = p → q
p | q | ~ p | ~p or q | p → q |
V | V | | | |
V | F | | | |
F | V | | | |
F | F | | | |

18. p ↔ q = (p →q) and (q →p)
p | q | p ↔ q | p →q | q → p | (p →q) and (q →p) |
V | V | | | | |
V | F | | | | |
F | V | || | |
F | F | | | | |

19. p xor q = (p or q) and ~(p and q)
p | q | p xor q | p or q | p and q | ~(p and q) | (p or q) and ~(p and q) |
V | V | | | | | |
V | F | | | | | |
F | V | | | | | |
F | F | | | | | |

20. p → q = ~(q) → ~(p)

p | q | p → q | ~(p) | ~(q) | ~(q) → ~(p) |
V | V | | | | |
V | F | | | | |
F | V | | | | |
F |F | | | | |

B. Construir las tablas de verdad de
21. ~p and q
p | q | ~p | ~p and q |
V | V | | |
V | F | | |
F | V | | |
F | F | | |

22. ~p and ~q
p | q | ~p | ~q | ~p and ~q |
V | V | | | |
V | F | | | |
F | V | | | |
F | F | | | |

23. [(p or ~(q)] or p

p | q | ~(q) | (p or ~(q) | [(p or ~(q)] or p |
V | V | | | |
V | F | |...