# Changes

,  02:06, 16 May 2012
update
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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.

'''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 '''&not;p''') is as follows:
+
The [[truth table]] of $\operatorname{NOT}~ p,$ also written $\lnot p,\!$ appears below:

<br>

<br>
−
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:40%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
|+ '''Logical Negation'''
+
|+ style="height:30px" | $\text{Logical Negation}\!$
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="width:20%" | p
+
| style="width:50%" | $p\!$
! style="width:20%" | &not;p
+
| style="width:50%" | $\lnot p\!$

|-

|-
| F || T
+
| $\operatorname{F}$ || $\operatorname{T}$

|-

|-
| T || F
+
| $\operatorname{T}$ || $\operatorname{F}$

|}

|}

<br>

<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:
+
The negation of a proposition $p\!$ may be found notated in various ways in various contexts of application, often merely for typographical convenience.  Among these variants are the following:

<br>

<br>
−
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; width:40%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" width="45%"
|+ '''Variant Notations'''
+
|+ style="height:30px" | $\text{Variant Notations}\!$
|- style="background:#e6e6ff"
+
|- style="height:40px; background:#f0f0ff"
! style="text-align:center" | Notation
+
| width="50%" align="center" | $\text{Notation}\!$
! Vocalization
+
| width="50%" | $\text{Vocalization}\!$

|-

|-
| style="text-align:center" | $\bar{p}$
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| align="center" | $\bar{p}\!$
| bar ''p''
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| $p\!$ bar

|-

|-
| style="text-align:center" | $p'\!$
+
| align="center" | $\tilde{p}\!$
| ''p'' prime,<p> ''p'' complement
+
| p\!</math> tilde |- |- | style="text-align:center" | [itex]!p\!
+
| align="center" | $p'\!$
| bang ''p''
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| $p\!$ prime<br> $p\!$ complement
+
|-
+
| align="center" | $!p\!$
+
| bang $p\!$

|}

|}

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