Tautologias
Tautologías
John Fredy Briñez Pantoja
Cód: 051100052011
Universidad del Tolima
Grupo 01 – Sem 1
1. (p V p) ↔ p ; (p ^ p) → p
p | p V p | (p V p) ↔ p |
V | V | V |
F | F | V |
p | p ^ p | (p ^ p) ↔ p |
V | V | V |
F | F | V |
2. p V q ↔ q V p
p | q | p V q | q V p | p V q ↔ q V p |
V | V | V | V | V |
V | F | V | V | V |
F | V| V | V | V |
f | f | f | f | V |
3. (p V q) V r ↔ p V (q V r)
p | q | r | p V q | (p V q) V r | q V r | p V (q V r) | (p V q) V r ↔ p V (q V r) |
V | V | V | V | V | V | V | V |
V | V | F | V | V | V | V | V |
V | F | V | V | V | V | V | V |
V | F | F | V | V | F | V | V |
F | V | V | V | V | V | V | V |
F | V | F | V | V | V | V | V |
F | F | V | F | V | V | V | V |
F |F | F | F | F | F | F | V |
4. 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) | p ^ (q V r) ↔ (p ^ q) V (p ^ r) |
V | V | V | V | V | V | V | V | V |
V | V | F | V | V | V | F | V | V |
V | F | V | V | V | F | V | V | V |
V | F | F | F | F | F | F | F | V |
F | V | V | V | F | F | F | F | V |
F | V | F | V | F | F | F | F | V |F | F | V | V | F | F | F | F | V |
F | F | F | F | F | F | F | F | V |
5. ¬ (p ^ q) ↔ (¬p V ¬q)
p | q | ¬(p ^ q) | ¬p | ¬q | ¬p V ¬q | ¬(p ^ q) ↔ (¬p V ¬q) |
V | V | F | F | F | F | V |
V | F | V | F | V | V | V |
F | V | V | V | F | V | V |
F | F | V | V | V | V | V |
6. (p ^ q) ^ r ↔ p ^ (q ^ r)
p | q | r | p ^ q | (p ^ q) ^ r | q ^ r | p ^ (q ^ r) | (p ^ q) ^ r ↔ p^ (q ^ r) |
V | V | V | V | V | V | V | V |
V | V | F | V | F | F | F | V |
V | F | V | F | F | F | F | V |
V | F | F | F | F | F | F | V |
F | V | V | F | F | V | F | V |
F | V | F | F | F | F | F | V |
F | F | V | F | F | F | F | V |
F | F | F | F | F | F | F | V |
7. (p ^ q) ^ p ↔ p ^ q
p | q | p ^ q | (p ^ q) ^ p | (p ^ q) ^ p ↔ p ^ q |
V | V | V | V | V |
V | F | F |F | V |
F | V | F | F | V |
F | F | F | F | V |
8. 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) | p ^ (q V r) ↔ (p ^ q) V (p ^ r) |
V | V | V | V | V | V | V | V | V |
V | V | F | V | V | V | F | V | V |
V | F | V | V | V | F | V | V | V |
V | F | F | F | F | F | F | F | V |
F | V | V | V | F | F | F | F | V |
F | V | F |V | F | F | F | F | V |
F | F | V | V | F | F | F | F | V |
F | F | F | F | F | F | F | F | V |
9. p V (q ^ r) ↔ (p V q) ^ (p V r)
p | q | r | q ^ r | p V (q ^ r) | p V q | p V r | (p V q) ^ (p V r) | p V (q ^ r) ↔ (p V q) ^ (p V r) |
V | V | V | V | V | V | V | V | V |
V | V | F | F | V | V | V | V | V |
V | F | V | F | V | V | V | V | V |
V | F | F | F | V | V | V | V | V |F | V | V | V | V | V | V | V | V |
F | V | F | F | F | V | F | F | V |
F | F | V | F | F | F | V | F | V |
F | F | F | F | F | F | F | F | V |
10. (p → (q → r) )↔ (p ^ q → r)
p | q | r | q → r | p → (q → r) | p ^ q | p ^ q → r | (p → (q → r) )↔ (p ^ q → r) |
V | V | V | V | V | V | V | V |
V | V | F | F | F | V | F | V |
V | F | V | V | V | F | V | V |
V | F | F | V | V | F | V| V |
F | V | V | V | V | F | V | V |
F | V | F | F | V | F | V | V |
F | F | V | V | V | F | V | V |
F | F | F | V | V | F | V | V |
11. [ p → (q → r)] → [(p → q )→ (p → r)]
p | q | r | q → r | p → (q → r) | p → q | p → r | [(p → q )→ (p → r)] | [ p → (q → r)] → [(p → q )→ (p → r)] |
V | V | V | V | V | V | V | V | V |
V | V | F | F | F | V | F | F | V |
V | F | V | V | V | F| V | V | V |
V | F | F | V | V | F | F | V | V |
F | V | V | V | V | V | V | V | V |
F | V | F | F | V | V | V | V | V |
F | F | V | V | V | V | V | V | V |
F | F | F | V | V | V | V | V | V |
12. ¬ (p ↔ q) ↔ ((p ^ ¬q) V (¬p ^ q))
p | q | ¬ (p ↔ q) | ¬p | ¬q | p ^ ¬q | ¬p ^ q | ((p ^ ¬q) V (¬p ^ q)) | ¬ (p ↔ q) ↔ ((p ^ ¬q) V (¬p ^ q)) |
V | V | F | F | F | F | F | F | V |
V |...
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