Difference between revisions of "Logical disjunction"

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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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'''Logical disjunction''', also called '''logical alternation''', is an [[logical operation|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 false.
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'''Logical disjunction''', also called '''logical alternation''', 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 false.
  
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The [[truth table]] of '''p OR q''' (also written as '''p &or; q''') is as follows:
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The [[truth table]] of <math>p ~\operatorname{OR}~ q,</math> also written <math>p \lor q,\!</math> appears below:
  
 
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<br>
  
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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 Disjunction'''
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|+ style="height:30px" | <math>\text{Logical Disjunction}\!</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 &or; q
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| style="width:33%" | <math>p \lor q</math>
 
|-
 
|-
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| F || F || F
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| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</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 || T
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| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</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_disjunction Logical Disjunction @ InterSciWiki]
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* [http://mywikibiz.com/Logical_disjunction Logical Disjunction @ MyWikiBiz]
 
* [http://mywikibiz.com/Logical_disjunction Logical Disjunction @ MyWikiBiz]
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* [http://mathweb.org/wiki/Logical_disjunction Logical Disjunction @ MathWeb Wiki]
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* [http://ref.subwiki.org/wiki/Logical_disjunction Logical Disjunction @ Subject Wikis]
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* [http://netknowledge.org/wiki/Logical_disjunction Logical Disjunction @ NetKnowledge]
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* [http://en.wikiversity.org/wiki/Logical_disjunction Logical Disjunction @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Logical_disjunction Logical Disjunction @ Wikiversity Beta]
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* [http://wiki.oercommons.org/mediawiki/index.php/Logical_disjunction Logical Disjunction @ OER Commons]
 
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* [http://p2pfoundation.net/Logical_Disjunction Logical Disjunction @ P2P Foundation]
 
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* [http://semanticweb.org/wiki/Logical_disjunction Logical Disjunction @ SemanticWeb]
 
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===Logical operators===
 
===Logical operators===
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* [[Inquiry]]
 
* [[Inquiry]]
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* [[Dynamics of inquiry]]
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* [[Semeiotic]]
 
* [[Logic of information]]
 
* [[Logic of information]]
 
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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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* [[Semeiotic]]
 
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* [[Semiotic information]]
 
 
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===Related articles===
 
===Related articles===
  
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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://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/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/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/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
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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_:_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/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&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://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&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://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&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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==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_disjunction Logical Disjunction], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Logical_disjunction Logical Disjunction], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Logical_disjunction Logical Disjunction], [http://mywikibiz.com/ MyWikiBiz]
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* [http://wikinfo.org/w/index.php/Logical_disjunction Logical Disjunction], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Logical_disjunction Logical Disjunction], [http://en.wikiversity.org/ Wikiversity]
 
* [http://beta.wikiversity.org/wiki/Logical_disjunction Logical Disjunction], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [http://beta.wikiversity.org/wiki/Logical_disjunction Logical Disjunction], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://getwiki.net/-Disjunction&r=Logical_disjunction Logical Disjunction], [http://getwiki.net/ GetWiki]
 
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* [http://wikinfo.org/index.php/Logical_disjunction Logical Disjunction], [http://wikinfo.org/ Wikinfo]
 
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* [http://textop.org/wiki/index.php?title=Logical_disjunction Logical Disjunction], [http://textop.org/wiki/ Textop Wiki]
 
 
* [http://en.wikipedia.org/w/index.php?title=Logical_disjunction&oldid=75154551 Logical Disjunction], [http://en.wikipedia.org/ Wikipedia]
 
* [http://en.wikipedia.org/w/index.php?title=Logical_disjunction&oldid=75154551 Logical Disjunction], [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 00:40, 2 November 2015

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

Logical disjunction, also called logical alternation, 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 false.

The truth table of \(p ~\operatorname{OR}~ q,\) also written \(p \lor q,\!\) appears below:


\(\text{Logical Disjunction}\!\)
\(p\!\) \(q\!\) \(p \lor q\)
\(\operatorname{F}\) \(\operatorname{F}\) \(\operatorname{F}\)
\(\operatorname{F}\) \(\operatorname{T}\) \(\operatorname{T}\)
\(\operatorname{T}\) \(\operatorname{F}\) \(\operatorname{T}\)
\(\operatorname{T}\) \(\operatorname{T}\) \(\operatorname{T}\)


Syllabus

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Logical operators

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Relational concepts

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Information, Inquiry

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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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