###### 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 |