Difference between revisions of "Logical NAND"

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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
 
<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
  
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The '''logical NAND''' is a [[logical operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if both of its operands are true.  In other words, it produces a value of ''true'' if and only if at least one of its operands is false.
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The '''logical NAND''' is an operation on two logical values, typically the values of two propositions, that produces a value of ''false'' if and only if both of its operands are true.  In other words, it produces a value of ''true'' if and only if at least one of its operands is false.
  
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The [[truth table]] of '''p NAND q''' (also written as '''p&nbsp;|&nbsp;q''' or '''p&nbsp;&uarr;&nbsp;q''') is as follows:
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The [[truth table]] of <math>p ~\operatorname{NAND}~ q,</math> also written <math>p \stackrel{\circ}{\curlywedge} q\!</math> or <math>p \barwedge q,\!</math> appears below:
  
 
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:45%"
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%"
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|+ '''Logical NAND'''
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|+ style="height:30px" | <math>\text{Logical NAND}\!</math>
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|- style="background:#e6e6ff"
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|- style="height:40px; background:#f0f0ff"
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! style="width:15%" | p
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| style="width:33%" | <math>p\!</math>
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! style="width:15%" | q
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| style="width:33%" | <math>q\!</math>
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! style="width:15%" | p &uarr; q
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| style="width:33%" | <math>p \stackrel{\circ}{\curlywedge} q\!</math>
 
|-
 
|-
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| F || F || T
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| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
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| F || T || T
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| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
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| T || F || T
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| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
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| T || T || F
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| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|}
 
|}
  
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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/Logical_NAND Logical NAND @ InterSciWiki]
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* [http://mywikibiz.com/Logical_NAND Logical NAND @ MyWikiBiz]
 
* [http://mywikibiz.com/Logical_NAND Logical NAND @ MyWikiBiz]
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* [http://mathweb.org/wiki/Logical_NAND Logical NAND @ MathWeb Wiki]
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* [http://ref.subwiki.org/wiki/Logical_NAND Logical NAND @ Subject Wikis]
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* [http://netknowledge.org/wiki/Logical_NAND Logical NAND @ NetKnowledge]
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* [http://en.wikiversity.org/wiki/Logical_NAND Logical NAND @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Logical_NAND Logical NAND @ Wikiversity Beta]
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* [http://wiki.oercommons.org/mediawiki/index.php/Logical_NAND Logical NAND @ OER Commons]
 
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* [http://p2pfoundation.net/Logical_NAND Logical NAND @ P2P Foundation]
 
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* [http://semanticweb.org/wiki/Logical_NAND Logical NAND @ SemanticWeb]
 
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===Logical operators===
 
===Logical operators===
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* [[Pragmatic maxim]]
 
* [[Pragmatic maxim]]
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* [[Pragmatic theory of truth]]
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* [[Truth theory]]
 
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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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{{col-break}}
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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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{{col-end}}
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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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{{col-begin}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Logical_NAND Logical NAND], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Logical_NAND Logical NAND], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Logical_NAND Logical NAND], [http://mywikibiz.com/ MyWikiBiz]
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* [http://wikinfo.org/w/index.php/Logical_NAND Logical NAND], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Logical_NAND Logical NAND], [http://en.wikiversity.org/ Wikiversity]
 
* [http://beta.wikiversity.org/wiki/Logical_NAND Logical NAND], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [http://beta.wikiversity.org/wiki/Logical_NAND Logical NAND], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://getwiki.net/-Logical_NAND Logical NAND], [http://getwiki.net/ GetWiki]
 
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* [http://wikinfo.org/index.php/Logical_NAND Logical NAND], [http://wikinfo.org/ Wikinfo]
 
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* [http://textop.org/wiki/index.php?title=Logical_NAND Logical NAND], [http://textop.org/wiki/ Textop Wiki]
 
 
* [http://en.wikipedia.org/w/index.php?title=Logical_NAND&oldid=75155132 Logical NAND], [http://en.wikipedia.org/ Wikipedia]
 
* [http://en.wikipedia.org/w/index.php?title=Logical_NAND&oldid=75155132 Logical NAND], [http://en.wikipedia.org/ Wikipedia]
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[[Category:Inquiry]]
 
[[Category:Inquiry]]
 
[[Category:Open Educational Resource]]
 
[[Category:Open Educational Resource]]
 
[[Category:Peer Educational Resource]]
 
[[Category:Peer Educational Resource]]
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[[Category:Charles Sanders Peirce]]
 
[[Category:Computer Science]]
 
[[Category:Computer Science]]
 
[[Category:Formal Languages]]
 
[[Category:Formal Languages]]

Latest revision as of 22:56, 4 November 2015

☞ This page belongs to resource collections on Logic and Inquiry.

The logical NAND is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are true. In other words, it produces a value of true if and only if at least one of its operands is false.

The truth table of \(p ~\operatorname{NAND}~ q,\) also written \(p \stackrel{\circ}{\curlywedge} q\!\) or \(p \barwedge q,\!\) appears below:


\(\text{Logical NAND}\!\)
\(p\!\) \(q\!\) \(p \stackrel{\circ}{\curlywedge} q\!\)
\(\operatorname{F}\) \(\operatorname{F}\) \(\operatorname{T}\)
\(\operatorname{F}\) \(\operatorname{T}\) \(\operatorname{T}\)
\(\operatorname{T}\) \(\operatorname{F}\) \(\operatorname{T}\)
\(\operatorname{T}\) \(\operatorname{T}\) \(\operatorname{F}\)


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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.

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