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# System prepended metadata

title: discrete logic 等值規則

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# discrete logic 等值規則

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|      | abbreviation(縮寫)or origin(出處) |    word   |   part of speech(詞性)   |   chinese   |   Notes(備註)造句   |
|   -   |   -   |   -   |   -   |   -   |   -   |
|   01.   |law of double negation|   DN.   |   -   |雙重否定|![](https://latex.codecogs.com/svg.image?\widetilde{\widetilde{p}}&space;\equiv&space;p)|
|   02.   |DeMorgan's laws|   DeM.   |   -   |迪摩根定理|![](https://latex.codecogs.com/svg.image?\widetilde{\left&space;(&space;p&space;\cup&space;q&space;\right&space;)}&space;\equiv&space;\widetilde{p}&space;\cap&space;&space;\widetilde{q}) ![](https://latex.codecogs.com/svg.image?\widetilde{\left&space;(&space;p&space;\cap&space;q&space;\right&space;)}&space;\equiv&space;\widetilde{p}&space;\cup&space;&space;\widetilde{q})|
|   03.   |commulative law|   Comm.   |   -   |交換律|![](https://latex.codecogs.com/svg.image?p&space;\cap&space;q&space;\equiv&space;q&space;\cap&space;p) ![](https://latex.codecogs.com/svg.image?p&space;\cup&space;q&space;\equiv&space;q&space;\cup&space;p)|
|   04.   |associative|   Assoc.   |   -   |結合律|![](https://latex.codecogs.com/svg.image?p\cap&space;\left&space;(&space;q\cap&space;r&space;\right&space;)&space;\equiv&space;\left&space;(&space;p\cap&space;q&space;\right&space;)&space;\cap&space;r) ![](https://latex.codecogs.com/svg.image?p\cup&space;\left&space;(&space;q\cup&space;r&space;\right&space;)&space;\equiv&space;\left&space;(&space;p\cup&space;q&space;\right&space;)&space;\cup&space;r)|
|   05.   |distributive|   Dist.   |   -   |分配律|![](https://latex.codecogs.com/svg.image?p&space;\cup&space;\left&space;(&space;q\cap&space;r&space;\right&space;)&space;\equiv&space;\left&space;(&space;p&space;\cup&space;q\right&space;)&space;\cap&space;\left&space;(&space;p&space;\cap&space;r&space;\right&space;)) ![](https://latex.codecogs.com/svg.image?p&space;\cap&space;\left&space;(&space;q\cup&space;r&space;\right&space;)&space;\equiv&space;\left&space;(&space;p&space;\cap&space;q\right&space;)&space;\cup&space;\left&space;(&space;p&space;\cup&space;r&space;\right&space;))|
|   06.   |idempotent law|   Taut.   |   恆真句   |自運算|![](https://latex.codecogs.com/svg.image?p&space;\cup&space;p&space;\equiv&space;p) ![](https://latex.codecogs.com/svg.image?p&space;\cap&space;p&space;\equiv&space;p)|
|   07.   |identity law| - | - |同一律|![](https://latex.codecogs.com/svg.image?p\cap&space;T&space;\equiv&space;p) ![](https://latex.codecogs.com/svg.image?p\cup&space;F&space;\equiv&space;p)|
|   08.   |inverse law|   -   |   -   |   -   |![](https://latex.codecogs.com/svg.image?p\cup&space;&space;\widetilde{p}&space;\equiv&space;T)  ![](https://latex.codecogs.com/svg.image?p\cap&space;\widetilde{p}&space;\equiv&space;F)|
|   09.   |domination law|   -   |   -   |   -   | ![](https://latex.codecogs.com/svg.image?p\cup&space;T&space;\equiv&space;T) ![](https://latex.codecogs.com/svg.image?p\cap&space;F&space;\equiv&space;F)|
|   10.   |absorption law|   -   |   -   |吸收律| ![](https://latex.codecogs.com/svg.image?p\cup&space;\left&space;(&space;p\cap&space;q&space;\right&space;)\equiv&space;p) ![](https://latex.codecogs.com/svg.image?p\cap&space;\left&space;(&space;q\cup&space;p&space;\right&space;)\equiv&space;p)|
|   11.   |principle of duality|   -   |   -   |對偶關係|   -   |
|   12.   |the implication|   -   |   -   |蘊含|p->q|
|   13.   |contrapositive|   ConTra.   |   -   |異值位換律|$p\rightarrow q\equiv \neg q \rightarrow \neg  p$|
|   14.   |converse|   -   |   -   |逆命題|q->p|
|   15.   |inverse|   -   |   -   |否定逆命題|~ p-> ~ q   -   |
|   16.   |exportation|Exp.|   -   |移出律|$(p\cap q)\rightarrow r\equiv p\rightarrow(q\rightarrow r)$|
|   17.   |inply|Inpl.|   -   |實質蘊含律|$p\rightarrow q\equiv\neg p\cup q$|
|   18.   |Equivalence|Equiv.|   -   |實質等值律|$p\leftrightarrow q\equiv (p\cap q)\cup(\neg p\cap\neg q)\equiv(p\rightarrow q)\cap(q\rightarrow p)$|
|   19.   |   -   |   -   |   -   |   -   |   -   |
|   20.   |   -   |   -   |   -   |   -   |   -   |
|    -    |   -   |   -   |   -   |   -   |   -   |


$1.(\neg E \rightarrow F)\cap (F\rightarrow E)\\
2. \neg E\cup F\\  
3. \neg F \\
\therefore E\cap F$



