Editing Negation (section)

==Notation==
The negation of a proposition {{mvar|p}} is notated in different ways, in various contexts of discussion and fields of application. The following table documents some of these variants:

{| class="wikitable"
|- style="background:paleturquoise"
! Notation
! Plain text
! Vocalization
|-
| style="text-align:center" | <math>\neg p</math>
| style="text-align:center" | {{mono|¬p}} , {{mono|7p}}<ref>Used as makeshift in early typewriter publications, e.g. {{cite journal | doi=10.1145/990518.990519 | author=Richard E. Ladner | title=The circuit value problem is log space complete for P | journal=ACM SIGACT News | volume=7 | number=101 | pages=18&ndash;20 | date=Jan 1975 }}</ref>
| Not ''p''
|-
| style="text-align:center" | <math>\mathord{\sim} p</math>
| style="text-align:center" | {{mono|~p}}
| Not ''p''
|-
| style="text-align:center" | <math>-p</math>
| style="text-align:center" | {{mono|-p}}
| Not ''p''
|-
| style="text-align:center" | <math>Np</math>
|
| En ''p''
|-
| style="text-align:center" | <math>p'</math>
| style="text-align:center" | {{mono|p'}}
| {{unbulleted list
 | ''p'' prime,
 | ''p'' complement
 }}
|-
| style="text-align:center" | <math>\overline{p}</math>
| style="text-align:center" | {{mono| ̅p}}
| {{unbulleted list
 | ''p'' bar,
 | Bar ''p''
 }}
|-
| style="text-align:center" | <math>!p</math>
| style="text-align:center" | {{mono|!p}}
| {{unbulleted list
 | Bang ''p''
 | Not ''p''
 }}
|-
|}

The notation <math>Np</math> is [[Polish notation#Polish notation for logic|Polish notation]].

In [[Set theory#Basic concepts and notation|set theory]], <math>\setminus</math> is also used to indicate 'not in the set of': <math>U \setminus A</math> is the set of all members of {{mvar|U}} that are not members of {{mvar|A}}.

Regardless how it is notated or [[List of logic symbols|symbolized]], the negation <math>\neg P</math> can be read as "it is not the case that {{mvar|P}}", "not that {{mvar|P}}", or usually more simply as "not {{mvar|P}}".

===Precedence===

{{See also|Logical connective#Order of precedence}}

As a way of reducing the number of necessary parentheses, one may introduce [[precedence rule]]s: &not; has higher precedence than &and;, &and; higher than &or;, and &or; higher than →. So for example, <math>P \vee Q \wedge{\neg R} \rightarrow S</math> is short for <math>(P \vee (Q \wedge (\neg R))) \rightarrow S.</math>

Here is a table that shows a commonly used precedence of logical operators.<ref>{{citation|title=Discrete Mathematics Using a Computer|first1=John|last1=O'Donnell|first2=Cordelia|last2=Hall|first3=Rex|last3=Page| publisher=Springer| year=2007| isbn=9781846285981|page=120|url=https://books.google.com/books?id=KKxyQQWQam4C&pg=PA120}}.</ref>
{| class="wikitable" style="text-align: center;"
!Operator !!Precedence
|-
| <math>\neg</math> || 1
|-
| <math>\land</math> || 2
|-
| <math>\lor</math> || 3
|-
| <math>\to</math> || 4
|-
| <math>\leftrightarrow</math> || 5
|}