# discrete logic 等值規則 [![hackmd-github-sync-badge](https://hackmd.io/fMuLKio4RF-YPn4aj4Ozlw/badge)](https://hackmd.io/fMuLKio4RF-YPn4aj4Ozlw) p80 ## 網站支援 [詞性縮寫總整理](https://boroenglish.com/詞性縮寫總整理/) [查察](https://tw.ichacha.net) [Cambridge Dictionary 劍橋字典](https://dictionary.cambridge.org/zht/) [quizlet](https://quizlet.com/latest) [雙語詞彙學術名詞暨辭資訊網](https://terms.naer.edu.tw/) [latex codecog](https://latex.codecogs.com) | | 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. | - | - | - | - | - | | - | - | - | - | - | - | $1.(\neg E \rightarrow F)\cap (F\rightarrow E)\\ 2. \neg E\cup F\\ 3. \neg F \\ \therefore E\cap F$