Difference between revisions of "Logical equality"

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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 equality''' is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both operands are false or both operands are true.
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'''Logical equality''' is an operation on two logical values, typically the values of two propositions, that produces a value of ''true'' if and only if both operands are false or both operands are true.
  
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The [[truth table]] of '''p EQ q''' (also written as '''p = q''', '''p &harr; q''', or '''p &equiv; q''') is as follows:
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The [[truth table]] of <math>p ~\operatorname{EQ}~ q,</math> also written <math>p = q,\!</math> <math>p \Leftrightarrow q,\!</math> or <math>p \equiv 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 Equality'''
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|+ style="height:30px" | <math>\text{Logical Equality}\!</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 = q
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| style="width:33%" | <math>p = 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 || F
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| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
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| T || F || F
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| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</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_equality Logical Equality @ InterSciWiki]
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* [http://mywikibiz.com/Logical_equality Logical Equality @ MyWikiBiz]
 
* [http://mywikibiz.com/Logical_equality Logical Equality @ MyWikiBiz]
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* [http://mathweb.org/wiki/Logical_equality Logical Equality @ MathWeb Wiki]
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* [http://ref.subwiki.org/wiki/Logical_equality Logical Equality @ Subject Wikis]
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* [http://netknowledge.org/wiki/Logical_equality Logical Equality @ NetKnowledge]
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* [http://en.wikiversity.org/wiki/Logical_equality Logical Equality @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Logical_equality Logical Equality @ Wikiversity Beta]
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* [http://wiki.oercommons.org/mediawiki/index.php/Logical_equality Logical Equality @ OER Commons]
 
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* [http://p2pfoundation.net/Logical_Equality Logical Equality @ P2P Foundation]
 
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* [http://semanticweb.org/wiki/Logical_equality Logical Equality @ SemanticWeb]
 
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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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{{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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* [http://intersci.ss.uci.edu/wiki/index.php/Logical_equality Logical Equality], [http://intersci.ss.uci.edu/ InterSciWiki]
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{{col-break}}
 
 
* [http://mywikibiz.com/Logical_equality Logical Equality], [http://mywikibiz.com/ MyWikiBiz]
 
* [http://mywikibiz.com/Logical_equality Logical Equality], [http://mywikibiz.com/ MyWikiBiz]
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* [http://wikinfo.org/w/index.php/Logical_equality Logical Equality], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Logical_equality Logical Equality], [http://en.wikiversity.org/ Wikiversity]
 
* [http://beta.wikiversity.org/wiki/Logical_equality Logical Equality], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [http://beta.wikiversity.org/wiki/Logical_equality Logical Equality], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [http://getwiki.net/-Logical_Equality Logical Equality], [http://getwiki.net/ GetWiki]
 
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* [http://wikinfo.org/index.php/Logical_equality Logical Equality], [http://wikinfo.org/ Wikinfo]
 
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* [http://textop.org/wiki/index.php?title=Logical_equality Logical Equality], [http://textop.org/wiki/ Textop Wiki]
 
 
* [http://en.wikipedia.org/w/index.php?title=Logical_equality&oldid=77110577 Logical Equality], [http://en.wikipedia.org/ Wikipedia]
 
* [http://en.wikipedia.org/w/index.php?title=Logical_equality&oldid=77110577 Logical Equality], [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 04:18, 4 November 2015

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

Logical equality is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false or both operands are true.

The truth table of \(p ~\operatorname{EQ}~ q,\) also written \(p = q,\!\) \(p \Leftrightarrow q,\!\) or \(p \equiv q,\!\) appears below:


\(\text{Logical Equality}\!\)
\(p\!\) \(q\!\) \(p = q\!\)
\(\operatorname{F}\) \(\operatorname{F}\) \(\operatorname{T}\)
\(\operatorname{F}\) \(\operatorname{T}\) \(\operatorname{F}\)
\(\operatorname{T}\) \(\operatorname{F}\) \(\operatorname{F}\)
\(\operatorname{T}\) \(\operatorname{T}\) \(\operatorname{T}\)


Syllabus

Focal nodes

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Logical operators

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Related topics

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Relational concepts

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Information, Inquiry

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Related articles

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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.

Retrieved from "https://mywikibiz.com/index.php?title=Logical_equality&oldid=466820"