---
# System prepended metadata

title: 2022/3/9 離散數學
tags: [110-2學校上課]

---

###### tags: `110-2學校上課`
# 2022/3/9 離散數學
### 表
1. "\wedge" = $\wedge$
2. "\vee"   = $\vee$
3. "\rightarrow" = $\rightarrow$
4. "\leftrightarrow" = $\leftrightarrow$
5. "\neg" = $\neg$
6. "\equiv" = $\equiv$
7. "\forall" = $\forall x$
8. "	\exists  " = $\exists x$
9. "\in"=$\in$

## Modus Ponens 肯定前件
$((p \wedge (p \rightarrow q)) \rightarrow q) \equiv T$  
 
 | p   | q   | $p \rightarrow q$ | $p \wedge (p \rightarrow q)$ | $(p \wedge (p \rightarrow q)) \rightarrow q$ |
 | --- | --- |:-----------------:|:---------------------------- |:--------------------------------------------:|
 | F   | F   |         T         | F                            |                      T                       |
 | F   | T   |         F         | F                            |                      T                       |
 | T   | F   |         T         | T                            |                      T                       |
 | T   | T   |         T         | T                            |                      T                       |



## Modus Tollens 否定後件
~p^(p->q)->~q
$(( \lrcorner p \wedge (p \rightarrow q)) \rightarrow \lrcorner q) \equiv T$  
 
 | p   | q   | $p \rightarrow q$ | $p \wedge (p \rightarrow q)$ | $(p \wedge (p \rightarrow q)) \rightarrow q$ |
 | --- | --- |:-----------------:|:---------------------------- |:--------------------------------------------:|
 | F   | F   |         T         | F                            |                      T                       |
 | F   | T   |         F         | F                            |                      T                       |
 | T   | F   |         T         | T                            |                      T                       |
 | T   | T   |         T         | T                            |                      T                       |

