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使用真值表方法判断以下公式
是 (1) 重言式、偶然式还是矛盾式 (2) 是否为逻辑真理 (3) 是否可满足：
1. [习题 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 |
重言式，可满足，逻辑真理
2. [习题 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 |
偶然式，可满足，非逻辑真理
3. [习题 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 |
偶然式，可满足，非逻辑真理
4. [习题 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 |
重言式，可满足，逻辑真理
5. [习题 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 |
偶然式，可满足，非逻辑真理
6. [习题 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 |
偶然式，可满足，非逻辑真理
7. [习题 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 |
重言式，可满足，逻辑真理
8. [习题 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 |
重言式，可满足，逻辑真理
9. [习题 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 |
矛盾式，不可满足，非逻辑真理
10. [习题 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 |
偶然式，可满足，非逻辑真理
11. [习题 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 |
偶然式，可满足，非逻辑真理
12. [习题 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 |
重言式，可满足，逻辑真理
13. [习题 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 |
偶然式，可满足，非逻辑真理
14. [习题 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 |
偶然式，可满足，非逻辑真理
15. [习题 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 |
重言式，可满足，逻辑真理（德摩根定律）
16. [习题 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 |
矛盾式，不可满足，非逻辑真理。
17. [习题 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 |
偶然式，可满足，非逻辑真理
18. [习题 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 |
偶然式，可满足，非逻辑真理。
19. [习题 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 |
偶然式，可满足，非逻辑真理
20. [习题 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 |
偶然式，可满足，非逻辑真理
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