Editing Logical NOR (section)

==Other Boolean operations in terms of the logical NOR==
NOR has the interesting feature that all other logical operators can be expressed by interlaced NOR operations. The [[logical NAND]] operator also has this ability.

Expressed in terms of NOR <math>\downarrow</math>, the usual operators of propositional logic are:

{|
|-
|<!--- not --->
{| style="text-align: center; border: 1px solid darkgray;"
|-
|<math>\neg P</math>
|&nbsp;&nbsp;&nbsp;&nbsp;<math>\Leftrightarrow</math>&nbsp;&nbsp;&nbsp;&nbsp;
|<math>P \downarrow P</math>
|-
|<math>\neg</math> [[File:Venn01.svg|36px]]
|&nbsp;&nbsp;&nbsp;&nbsp;<math>\Leftrightarrow</math>&nbsp;&nbsp;&nbsp;&nbsp;
|[[File:Venn10.svg|36px]]
|}<!--- end not--->
|&nbsp;&nbsp;&nbsp;
|<!--- arrow --->
{| style="text-align: center; border: 1px solid darkgray;" 
|-
|<math>P \rightarrow Q</math>
|&nbsp;&nbsp;&nbsp;&nbsp;<math>\Leftrightarrow</math>&nbsp;&nbsp;&nbsp;&nbsp;
|<math>\Big( (P \downarrow P) \downarrow Q \Big)</math>
|<math>\downarrow</math>
|<math>\Big( (P \downarrow P) \downarrow Q \Big)</math>
|-
|[[File:Venn1011.svg|50px]]
|&nbsp;&nbsp;&nbsp;&nbsp;<math>\Leftrightarrow</math>&nbsp;&nbsp;&nbsp;&nbsp;
|[[File:Venn0100.svg|50px]]
|<math>\downarrow</math>
|[[File:Venn0100.svg|50px]]
|}<!--- end arrow --->
|-
|&nbsp;
|-
|<!--- and --->
{| style="text-align: center; border: 1px solid darkgray;" 
|-
|<math>P \land Q</math>
|&nbsp;&nbsp;&nbsp;&nbsp;<math>\Leftrightarrow</math>&nbsp;&nbsp;&nbsp;&nbsp;
|<math>(P \downarrow P)</math> 
|<math>\downarrow</math> 
|<math>(Q \downarrow Q)</math>
|-
|[[File:Venn0001.svg|50px]]
|&nbsp;&nbsp;&nbsp;&nbsp;<math>\Leftrightarrow</math>&nbsp;&nbsp;&nbsp;&nbsp;
|[[File:Venn1010.svg|50px]] 
|<math>\downarrow</math> 
|[[File:Venn1100.svg|50px]]
|}<!--- end and --->
|&nbsp;&nbsp;&nbsp;
|<!--- or --->
{| style="text-align: center; border: 1px solid darkgray;" 
|-
|<math>P \lor Q</math>
|&nbsp;&nbsp;&nbsp;&nbsp;<math>\Leftrightarrow</math>&nbsp;&nbsp;&nbsp;&nbsp;
|<math>(P \downarrow Q)</math> 
|<math>\downarrow</math> 
|<math>(P \downarrow Q)</math> 
|-
|[[File:Venn0111.svg|50px]]
|&nbsp;&nbsp;&nbsp;&nbsp;<math>\Leftrightarrow</math>&nbsp;&nbsp;&nbsp;&nbsp;
|[[File:Venn1000.svg|50px]] 
|<math>\downarrow</math> 
|[[File:Venn1000.svg|50px]] 
|}<!--- end or --->
|}