Adapte os exercícios resolvidos à sua disciplina. Registe-se gratuitamente
Descubra atraves do procedimento de tabelas de verdade
se estas formulas sao (1) tautologicas, contingentes ou contraditorias (2) Verdade logica ou nao, (3) Satisfaziveis ou nao :
1. [Exercício 1] p ∧ q → p
| p | q | p∧q | p ∧ q → p |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 0 | 0 | 1 |
TAUTOLOGIA, SATISFAZIVEL E VERDADE LOGICA
2. [Exercício 2] p ∨ p → r
| p | r | p ∨ p | p ∨ p → r |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 0 | 0 | 1 |
CONTINGENCIA, SATISFAZIVEL, NAO VERDADE LOGICA
3. [Exercicio 3]p ∨ (q → r)
| p | q | r | q → r | p ∨ (q → r) |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 0 | 0 | 1 | 1 |
CONTINGENTE, SATISFAZIVEL, NAO VERDADE LOGICA
4. [Exercicio 4](p → q) ∧ (q → r) → (p → r)
| p | q | r | p → q | q → r | (p → q) ∧ (q → r) | p → r | (p → q) ∧ (q → r) → (p → r) |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
5. [Exercicio 5]p → (q → r)
| p | q | r | q → r | p → (q → r) |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 1 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 0 | 0 | 1 | 1 |
CONTINGENTE, SATISFAZIVEL, NAO VERDADE LOGICA
6. [Exercicio 6]p ∨ q → (r ∨ s → p)
| p | q | r | s | p ∨ q | r ∨ s | r ∨ s → p | p ∨ q → (r ∨ s → p) |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
| 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 |
| 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
CONTINGENTE, SATISFAZIVEL, NAO VERDADE LOGICA
7. [Exercicio 7]p ∧ q → q ∧ p
| p | q | p ∧ q | q ∧ p | p ∧ q → q ∧ p |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 |
8. [Exercicio 8](p → q) ∧ p → q
| p | q | p → q | (p → q) ∧ p | (p → q) ∧ p → q |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 0 | 0 | 1 | 0 | 1 |
TAUTOLOGIA, SATISFAZIVEL, VERDADE LOGICA
9. [Exercicio 9](p → q) ∧ p ∧ ¬q
| p | q | ¬q | p → q | (p → q) ∧ p | (p → q) ∧ p ∧ ¬q |
|---|---|---|---|---|---|
| 1 | 1 | 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 |
CONTRADICAO, INSATISFAZIVEL, NAO VERDADE LOGICA
10. [Exercicio 10](p → q) ∧ (p → q)
| p | q | p → q | (p → q) ∧ (p → q) |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 |
11. [Exercicio 11](p → q) ∧ q → p
| p | q | p → q | (p → q) ∧ q | (p → q) ∧ q → p |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 |
| 0 | 0 | 1 | 0 | 1 |
CONTINGENTE, SATISFAZIVEL, NAO VERDADE LOGICA
12. [Exercicio 12](p → q) ∧ ¬q → ¬p
| p | q | ¬p | ¬q | p → q | p → q ∧ ¬q | (p → q) ∧ ¬q → ¬p |
|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 1 |
| 0 | 0 | 1 | 1 | 1 | 1 | 1 |
13. [Exercicio 13](p → q) ∧ ¬p → ¬q
| p | q | ¬p | ¬q | p → q | (p → q) ∧ ¬p | (p → q) ∧ ¬p → ¬q |
|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 | 1 | 1 | 0 |
| 0 | 0 | 1 | 1 | 1 | 1 | 1 |
CONTINGENTE, SATISFAZIVEL, NAO VERDADE LOGICA
14. [Exercicio 14]¬(p ∧ q) ↔ ¬p ∧ ¬q
| p | q | ¬p | ¬q | ¬p ∧ ¬q | p ∧ q | ¬(p ∧ q) | ¬(p ∧ q) ↔ ¬p ∧ ¬q |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
15. [Exercicio 15]¬(p ∧ q) ↔ ¬p ∨ ¬q
| p | q | ¬p | ¬q | p ∧ q | ¬(p ∧ q) | ¬p ∨ ¬q | ¬(p ∧ q) ↔ ¬p ∨ ¬q |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 |
TAUTOLOGIA, SATISFAZIVEL, VERDADE LOGICA (Lei de De Morgan)
16. [Exercicio 16][(p → q) ∧ (q → r)] ∧ ¬(p → r)
| p | q | r | p → q | q → r | p → q ∧ q → r | p → r | ¬(p → r) | (p → q) ∧ (q → r)] ∧ ¬(p → r) |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 |
17. [Exercicio 17]p → (q ∧ ¬r → ¬q)
| p | q | r | ¬r | ¬q | q ∧ ¬r | q ∧ ¬r → ¬q | p → (q ∧ ¬r → ¬q) |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
| 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
| 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
CONTINGENTE, SATISFAZIVEL, NAO VERDADE LOGICA
18. [Exercicio 18]¬(p ∨ q) ↔ ¬r ∨ ¬q
| p | q | r | ¬r | ¬q | p ∨ q | ¬(p ∨ q) | ¬r ∨ ¬q | ¬(p ∨ q) ↔ ¬r ∨ ¬q |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 |
| 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 |
19. [Exercicio 19]¬(p ∨ q) ↔ ¬p ∨ ¬r
| p | q | r | ¬p | ¬r | p ∨ q | ¬(p ∨ q) | ¬p ∨ ¬r | ¬(p ∨ q) ↔ ¬p ∨ ¬r |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |
| 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 |
CONTINGENTE, SATISFAZIVEL, NAO VERDADE LOGICA
20. [Exercicio 20] ¬(p → q) ↔ (p ∧ r)
| p | q | r | p ∧ r | p → q | ¬(p → q) | ¬(p → q) ↔ p ∧ r |
|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 1 | 0 | 1 |
| 0 | 0 | 1 | 0 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 | 1 |