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
TAUTOLOGICA, SATISFAZIVEL E VERDADE LOGICA

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
TAUTOLOGICA, SATISFAZIVEL, VERDADE LOGICA

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
CONTINGENTE, SATISFAZIVEL, NAO VERDADE LOGICA

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
TAUTOLOGICA, SATISFAZIVEL E VERDADE LOGICA

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
CONTINGENTE, SATISFAZIVEL E NAO VERDADE LOGICA

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
CONTRADICAO, INSATISFAZIVEL E NAO VERDADE LOGICA.

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
CONTINGENTE, SATISFAZIVEL E NAO VERDADE LOGICA.

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
CONTINGENTE, SATISFAZIVEL, NAO VERDADE LOGICA

 

 

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