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Truth table (view source)

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A '''truth table''' is a tabular array that illustrates the computation of a ''logical function'', that is, a function of the form <math>f : \mathbb{A}^k \to \mathbb{A},</math> where <math>k\!</math> is a non-negative integer and <math>\mathbb{A}</math> is the domain of logical values <math>\{ \operatorname{false}, \operatorname{true} \}.</math>  The names of the logical values, or ''truth values'', are commonly abbreviated in accord with the equations <math>\operatorname{F} = \operatorname{false}</math> and <math>\operatorname{T} = \operatorname{true}.</math>
 
A '''truth table''' is a tabular array that illustrates the computation of a ''logical function'', that is, a function of the form <math>f : \mathbb{A}^k \to \mathbb{A},</math> where <math>k\!</math> is a non-negative integer and <math>\mathbb{A}</math> is the domain of logical values <math>\{ \operatorname{false}, \operatorname{true} \}.</math>  The names of the logical values, or ''truth values'', are commonly abbreviated in accord with the equations <math>\operatorname{F} = \operatorname{false}</math> and <math>\operatorname{T} = \operatorname{true}.</math>
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In many applications it is usual to represent a truth function by a [[boolean function]], that is, a function of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>k\!</math> is a non-negative integer and <math>\mathbb{B}</math> is the [[boolean domain]] <math>\{ 0, 1 \}.\!</math>  In most applications the lo<math>\operatorname{false}</math> is represented by <math>0\!</math> and <math>\operatorname{true}</math> is represented by <math>1\!</math> but the opposite representation is also possible, depending on the overall representation of truth functions as boolean functions.  The remainder of this article assumes the usual representation, taking the equations <math>\operatorname{F} = 0</math> and <math>\operatorname{T} = 1</math> for granted.
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In many applications it is usual to represent a truth function by a [[boolean function]], that is, a function of the form <math>f : \mathbb{B}^k \to \mathbb{B},</math> where <math>k\!</math> is a non-negative integer and <math>\mathbb{B}</math> is the [[boolean domain]] <math>\{ 0, 1 \}.\!</math>  In most applications <math>\operatorname{false}</math> is represented by <math>0\!</math> and <math>\operatorname{true}</math> is represented by <math>1\!</math> but the opposite representation is also possible, depending on the overall representation of truth functions as boolean functions.  The remainder of this article assumes the usual representation, taking the equations <math>\operatorname{F} = 0</math> and <math>\operatorname{T} = 1</math> for granted.
    
==Logical negation==
 
==Logical negation==
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===Focal nodes===
 
===Focal nodes===
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* [[Inquiry Live]]
 
* [[Inquiry Live]]
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* [[Logic Live]]
 
* [[Logic Live]]
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===Peer nodes===
 
===Peer nodes===
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* [http://intersci.ss.uci.edu/wiki/index.php/Truth_table Truth Table @ InterSciWiki]
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* [http://mywikibiz.com/Truth_table Truth Table @ MyWikiBiz]
 
* [http://mywikibiz.com/Truth_table Truth Table @ MyWikiBiz]
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* [http://mathweb.org/wiki/Truth_table Truth Table @ MathWeb Wiki]
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* [http://netknowledge.org/wiki/Truth_table Truth Table @ NetKnowledge]
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* [http://wiki.oercommons.org/mediawiki/index.php/Truth_table Truth Table @ OER Commons]
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* [http://p2pfoundation.net/Truth_Table Truth Table @ P2P Foundation]
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* [http://semanticweb.org/wiki/Truth_table Truth Table @ SemanticWeb]
   
* [http://ref.subwiki.org/wiki/Truth_table Truth Table @ Subject Wikis]
 
* [http://ref.subwiki.org/wiki/Truth_table Truth Table @ Subject Wikis]
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* [http://en.wikiversity.org/wiki/Truth_table Truth Table @ Wikiversity]
 
* [http://beta.wikiversity.org/wiki/Truth_table Truth Table @ Wikiversity Beta]
 
* [http://beta.wikiversity.org/wiki/Truth_table Truth Table @ Wikiversity Beta]
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===Logical operators===
 
===Logical operators===
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===Related articles===
 
===Related articles===
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Semiotic_Information Jon Awbrey, &ldquo;Semiotic Information&rdquo;]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Introduction To Inquiry Driven Systems&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
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* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, &ldquo;Prospects For Inquiry Driven Systems&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, &ldquo;Inquiry Driven Systems : Inquiry Into Inquiry&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
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* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
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* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
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* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
      
==Document history==
 
==Document history==
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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.
 
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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* [http://intersci.ss.uci.edu/wiki/index.php/Truth_table Truth Table], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Truth_table Truth Table], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Truth_table Truth Table], [http://mywikibiz.com/ MyWikiBiz]
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* [http://mathweb.org/wiki/Truth_table Truth Table], [http://mathweb.org/ MathWeb Wiki]
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* [http://netknowledge.org/wiki/Truth_table Truth Table], [http://netknowledge.org/ NetKnowledge]
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* [http://wiki.oercommons.org/mediawiki/index.php/Truth_table Truth Table], [http://wiki.oercommons.org/ OER Commons]
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* [http://p2pfoundation.net/Truth_Table Truth Table], [http://p2pfoundation.net/ P2P Foundation]
   
* [http://semanticweb.org/wiki/Truth_table Truth Table], [http://semanticweb.org/ SemanticWeb]
 
* [http://semanticweb.org/wiki/Truth_table Truth Table], [http://semanticweb.org/ SemanticWeb]
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* [http://wikinfo.org/w/index.php/Truth_table Truth Table], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Truth_table Truth Table], [http://en.wikiversity.org/ Wikiversity]
 
* [http://beta.wikiversity.org/wiki/Truth_table Truth Table], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [http://beta.wikiversity.org/wiki/Truth_table Truth Table], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://getwiki.net/-Truth_Table Truth Table], [http://getwiki.net/ GetWiki]
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* [http://wikinfo.org/index.php/Truth_table Truth Table], [http://wikinfo.org/ Wikinfo]
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* [http://textop.org/wiki/index.php?title=Truth_table Truth Table], [http://textop.org/wiki/ Textop Wiki]
   
* [http://en.wikipedia.org/w/index.php?title=Truth_table&oldid=77110085 Truth Table], [http://en.wikipedia.org/ Wikipedia]
 
* [http://en.wikipedia.org/w/index.php?title=Truth_table&oldid=77110085 Truth Table], [http://en.wikipedia.org/ Wikipedia]
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[[Category:Inquiry]]
 
[[Category:Inquiry]]
Jon Awbrey
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