###### tags: `CISC1002` `chapter1-1`
# Propositions - Logical Operations
* Negation (“非”) : ¬p
* Conjunction (“并且”又称”合取”) : p /\\ q
* Disjunction (“或者”又称”析”取) : p \\/ q
* Exclusive (“异或”) : p $\bigoplus$ q
</br>
* Implication (“蕴含”) : p → q
* Biconditional (“当且仅当”又称”等价”) : p↔q

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## Truth table
* Negation Truth table

|p|¬q|
|:-:|:-:|
|T|F|
|F|T|
* Conjunction Truth table

|p|q|p /\\ q|
|:-:|:-:|:-:|
|T|T|T|
|T|F|F|
|F|T|F|
|F|F|F|

* Disjunction Truth table

|p|q|p\\/q|
|:-:|:-:|:-:|
|T|T|T|
|T|F|T|
|F|T|T|
|F|F|F|

* Exclusive Truth table

|p|q|p $\bigoplus$ q|
|:-:|:-:|:-:|
|T|T|F|
|T|F|T|
|F|T|T|
|F|F|F|

* Implication Truth table

|p|q|p→q|
|:-:|:-:|:-:|
|T|T|T|
|T|F|F|
|F|T|T|
|F|F|T|

* Biconditional Truth table

|p|q|p↔q|
|:-:|:-:|:-:|
|T|T|T|
|T|F|F|
|F|T|F|
|F|F|F|
---
## Precedence(優先順序) of Logical Operations
|Operatop|Precendence|
|:-:|:-:|
| ¬|1|
| /\\|2|
| \\/|3|
| →|4|
| ↔|5|

* ¬ $>$ /\\ $>$\\/ $>$ → $>$ ↔