Logica Matematica

Lógica Matemática taller No.2
10. Complete la siguiente tabla de verdad
p | q | r | ¬p | ¬q | ¬r | (p v ¬q) | (r ¬q) | (p q) (¬r ¬q) | ¬[ (p^¬q) (r¬q) ] |
V | V | V | F | F | F | V | F | V | F |
V | V | F | F | F | V | V | V | F | V |
V | F | V | F | V | F | V | V | V | F |
V | F | F | F | V | V | V |V | V | F |
F | V | V | V | F | F | F | F | V | F |
F | V | F | V | F | V | F | V | F | V |
F | F | V | V | V | F | V | V | F | V |
F | F | F | v | F | V| V | V | F | V |

14. Demostrar que las siguientes proposiciones son equivalentes
a. p ^ (q v r) ≡ (p ^q) v ( p ^r)
p | q | r | (q v r) | P ^ (q v r) | ≡ | (p ^q) | (p ^ r) | (p ^q) v (p^ r) |
V | V | V | V | V | ≡ | V | V | V |
V | V | F | V | V | ≡ | V | F | V |
V | F | V | V | V | ≡ | F | V | V |
V | F | F | F | F | ≡ | F | F | F |
F | V | V | V | F | ≡ | F | F | F |F | V | F | V | F | ≡ | F | F | F |
F | F | V | V | F | ≡ | F | F | F |
F | F | F | F | F | ≡ | F | F | F |

b. (p ^q) r ≡ (p r) v (q r)
p | q | r | (p ^q) |

(p ^q)r | ≡ | (p r) | (q r) | (p r) v (q r) |
V | V | V | V | V | ≡ | V | V | V |
V | V | F | V | F | ≡ | F | F | F |
V | F | V | F | V | ≡ | V | V | V |
V | F | F | F | V | ≡ | F |V | V |
F | V | V | F | V | ≡ | V | V | V |
F | V | F | F | V | ≡ | V | F | V |
F | F | V | F | V | ≡ | V | V | V |
F | F | F | F | V | ≡ | V | V | V |



c. [ ( p q) r]≡ [(p ^ ¬r) ¬q]

p | q | r | ¬q | ¬r | ( p q) | [(p q) r] | / | (p ^¬ r) | [(p ^ ¬ r) ¬q)] |
V | V | V | F | F | V | V | / | F | V |
V | V | F | F | V| V | F | / | V | F |
V | F | V | V | F | F | V | / | F | V |
V | F | F | V | V | F | V | / | V | V |
F | V | V | F | F | V | V | / | F | V |
F | V | F | F | V | V | F | / | F | V |
F...