不使用LEM规则证明p -> q |- -p v q
时间: 2024-01-16 10:03:06 浏览: 126
我们可以使用矛盾证明法来证明$p \to q \vdash \neg p \lor q$:
1. 假设$p \to q$为真且$\neg(\neg p \lor q)$为真。
2. 根据De Morgan定律,$\neg(\neg p \lor q)$等价于$p \land \neg q$。
3. 由1可知,$p \to q$为真,因此当$p$为真时,$q$也为真。
4. 由2可知,$\neg q$为真,因此$q$为假。
5. 由3和4可知,当$p$为真时,$q$为假,与$p \to q$为真矛盾。
6. 因此,假设$p \to q$为真且$\neg(\neg p \lor q)$为真的假设不成立,即$p \to q \vdash \neg p \lor q$成立。
因此,我们证明了$p \to q \vdash \neg p \lor q$。
相关问题
Show+that+a+formula+is+valid+iff+T=where+Tis+an+abbreviation+for+aninstance+p+V-p+ofLEM.
To show that a formula is valid if and only if T, where T is an abbreviation for an instance p V ~p of LEM, we can use the following steps:
1. Assume that the formula is valid.
2. By definition, a formula is valid if it is true in all interpretations.
3. Let p be a propositional variable.
4. Consider the interpretation I such that I(p) = true.
5. Since the formula is valid, it must be true in I.
6. Therefore, the formula (p V ~p) is true in I.
7. Since I(p) = true, we have (p V ~p) = true.
8. Now consider the interpretation J such that J(p) = false.
9. Again, since the formula is valid, it must be true in J.
10. Therefore, the formula (p V ~p) is true in J.
11. Since J(p) = false, we have (~p) = true.
12. Therefore, (p V ~p) = true in both cases where p is true and where p is false.
13. Thus, (p V ~p) is a tautology and T is true.
14. Conversely, assume that T is true.
15. Then (p V ~p) is a tautology.
16. Let I be an arbitrary interpretation.
17. If I(p) = true, then (p V ~p) = true by the tautology.
18. If I(p) = false, then (~p) = true by the tautology.
19. Therefore, (p V ~p) is true in all interpretations and the formula is valid.
lem5小波基函数如何在python
在Python中,可以使用PyWavelets库来实现小波变换,其中包含了Lemarie小波基函数。以下是使用PyWavelets库进行Lemarie小波变换的示例代码:
```python
import pywt
import numpy as np
# 构造信号
signal = np.array([1, 2, 3, 4, 5, 6, 7, 8])
# 构造小波基函数
wavelet = pywt.Wavelet('lemarie')
# 进行一级小波变换
coefficients = pywt.wavedec(signal, wavelet, level=1)
# 打印出变换后的系数
print(coefficients)
```
在上述代码中,我们首先构造了一个长度为8的信号,然后使用PyWavelets库中的`Wavelet`函数构造了Lemarie小波基函数。接着,我们使用`wavedec`函数对信号进行了一级小波变换,并将变换后的系数存储在`coefficients`变量中。最后,我们打印出了变换后的系数。