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MyWikiBiz, Author Your Legacy — Thursday November 14, 2024
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'''Logical negation''' is an [[logical operation|operation]] on one [[logical value]], typically the value of a [[proposition]], that produces a value of ''true'' when its operand is false and a value of ''false'' when its operand is true.
The [[truth table]] of '''NOT p''' (also written as '''~p''' or '''¬p''') is as follows:
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:40%"
|+ '''Logical Negation'''
|- style="background:paleturquoise"
! style="width:20%" | p
! style="width:20%" | ¬p
|-
| F || T
|-
| T || F
|}
<br>
The logical negation of a proposition '''p''' is notated in different ways in various contexts of discussion and fields of application. Among these variants are the following:
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; width:40%"
|+ '''Variant Notations'''
|- style="background:paleturquoise"
! style="text-align:center" | Notation
! Vocalization
|-
| style="text-align:center" | <math>\bar{p}</math>
| bar ''p''
|-
| style="text-align:center" | <math>p'\!</math>
| ''p'' prime,<p> ''p'' complement
|-
| style="text-align:center" | <math>!p\!</math>
| bang ''p''
|}
<br>
==See also==
===Logical operators===
{|
| valign=top |
* [[Exclusive disjunction]]
* [[Logical conjunction]]
* [[Logical disjunction]]
* [[Logical equality]]
| valign=top |
* [[Logical implication]]
* [[Logical NAND]]
* [[Logical NNOR]]
* [[Logical negation|Negation]]
|}
===Related topics===
{|
| valign=top |
* [[Ampheck]]
* [[Boolean algebra]]
* [[Boolean domain]]
* [[Boolean function]]
| valign=top |
* [[Boolean logic]]
* [[Laws of Form]]
* [[Logic gate]]
* [[Logical graph]]
| valign=top |
* [[Peirce's law]]
* [[Propositional calculus]]
* [[Sole sufficient operator]]
* [[Zeroth order logic]]
|}
The [[truth table]] of '''NOT p''' (also written as '''~p''' or '''¬p''') is as follows:
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:40%"
|+ '''Logical Negation'''
|- style="background:paleturquoise"
! style="width:20%" | p
! style="width:20%" | ¬p
|-
| F || T
|-
| T || F
|}
<br>
The logical negation of a proposition '''p''' is notated in different ways in various contexts of discussion and fields of application. Among these variants are the following:
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; width:40%"
|+ '''Variant Notations'''
|- style="background:paleturquoise"
! style="text-align:center" | Notation
! Vocalization
|-
| style="text-align:center" | <math>\bar{p}</math>
| bar ''p''
|-
| style="text-align:center" | <math>p'\!</math>
| ''p'' prime,<p> ''p'' complement
|-
| style="text-align:center" | <math>!p\!</math>
| bang ''p''
|}
<br>
==See also==
===Logical operators===
{|
| valign=top |
* [[Exclusive disjunction]]
* [[Logical conjunction]]
* [[Logical disjunction]]
* [[Logical equality]]
| valign=top |
* [[Logical implication]]
* [[Logical NAND]]
* [[Logical NNOR]]
* [[Logical negation|Negation]]
|}
===Related topics===
{|
| valign=top |
* [[Ampheck]]
* [[Boolean algebra]]
* [[Boolean domain]]
* [[Boolean function]]
| valign=top |
* [[Boolean logic]]
* [[Laws of Form]]
* [[Logic gate]]
* [[Logical graph]]
| valign=top |
* [[Peirce's law]]
* [[Propositional calculus]]
* [[Sole sufficient operator]]
* [[Zeroth order logic]]
|}
