Difference between revisions of "Logical negation"
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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 | + | The [[truth table]] of <math>\operatorname{NOT}~ p,</math> also written <math>\lnot p,\!</math> appears below: |
<br> | <br> | ||
| − | {| align="center" border="1" cellpadding="8" cellspacing="0" style=" | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%" |
| − | |+ | + | |+ style="height:30px" | <math>\text{Logical Negation}\!</math> |
| − | |- style="background:# | + | |- style="height:40px; background:#f0f0ff" |
| − | + | | style="width:50%" | <math>p\!</math> | |
| − | + | | style="width:50%" | <math>\lnot p\!</math> | |
|- | |- | ||
| − | | F || T | + | | <math>\operatorname{F}</math> || <math>\operatorname{T}</math> |
|- | |- | ||
| − | | T || F | + | | <math>\operatorname{T}</math> || <math>\operatorname{F}</math> |
|} | |} | ||
<br> | <br> | ||
| − | The | + | The negation of a proposition <math>p\!</math> 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" | + | {| align="center" border="1" cellpadding="8" cellspacing="0" width="45%" |
| − | |+ | + | |+ style="height:30px" | <math>\text{Variant Notations}\!</math> |
| − | |- style="background:# | + | |- style="height:40px; background:#f0f0ff" |
| − | + | | width="50%" align="center" | <math>\text{Notation}\!</math> | |
| − | ! | + | | width="50%" | <math>\text{Vocalization}\!</math> |
|- | |- | ||
| − | | | + | | align="center" | <math>\bar{p}\!</math> |
| − | | bar | + | | <math>p\!</math> bar |
|- | |- | ||
| − | | | + | | align="center" | <math>\tilde{p}\!</math> |
| − | | | + | | <math>p\!</math> tilde |
|- | |- | ||
| − | | | + | | align="center" | <math>p'\!</math> |
| − | | bang | + | | <math>p\!</math> prime<br> <math>p\!</math> complement |
| + | |- | ||
| + | | align="center" | <math>!p\!</math> | ||
| + | | bang <math>p\!</math> | ||
|} | |} | ||
Revision as of 02:06, 16 May 2012
☞ This page belongs to resource collections on Logic and Inquiry.
Logical negation is an 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 \(\operatorname{NOT}~ p,\) also written \(\lnot p,\!\) appears below:
| \(p\!\) | \(\lnot p\!\) |
| \(\operatorname{F}\) | \(\operatorname{T}\) |
| \(\operatorname{T}\) | \(\operatorname{F}\) |
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:
| \(\text{Notation}\!\) | \(\text{Vocalization}\!\) |
| \(\bar{p}\!\) | \(p\!\) bar |
| \(\tilde{p}\!\) | \(p\!\) tilde |
| \(p'\!\) | \(p\!\) prime \(p\!\) complement |
| \(!p\!\) | bang \(p\!\) |
Syllabus
Focal nodes
Template:Col-breakTemplate:Col-breakTemplate:Col-endPeer nodes
Logical operators
Related topics
- Propositional calculus
- Sole sufficient operator
- Truth table
- Universe of discourse
- Zeroth order logic
Relational concepts
Information, Inquiry
Related articles
Document history
Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.
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