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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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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
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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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'''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 <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:
    
<br>
 
<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%"
|+ '''Logical Equality'''
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|+ style="height:30px" | <math>\text{Logical Equality}\!</math>
|- style="background:#e6e6ff"
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|- style="height:40px; background:#f0f0ff"
! style="width:15%" | p
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| style="width:33%" | <math>p\!</math>
! style="width:15%" | q
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| style="width:33%" | <math>q\!</math>
! style="width:15%" | p = q
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| style="width:33%" | <math>p = q\!</math>
 
|-
 
|-
| F || F || T
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| <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math>
 
|-
 
|-
| F || T || F
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| <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || F || F
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| <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math>
 
|-
 
|-
| T || T || T
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| <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math>
 
|}
 
|}
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==Syllabus==
 
==Syllabus==
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===Focal nodes===
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* [[Inquiry Live]]
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* [[Logic Live]]
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===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]
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* [http://ref.subwiki.org/wiki/Logical_equality Logical Equality @ Subject Wikis]
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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]
    
===Logical operators===
 
===Logical operators===
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* [[Boolean function]]
 
* [[Boolean function]]
 
* [[Boolean-valued function]]
 
* [[Boolean-valued function]]
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* [[Differential logic]]
 
{{col-break}}
 
{{col-break}}
 
* [[Logical graph]]
 
* [[Logical graph]]
* [[Logical matrix]]
   
* [[Minimal negation operator]]
 
* [[Minimal negation operator]]
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* [[Multigrade operator]]
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* [[Parametric operator]]
 
* [[Peirce's law]]
 
* [[Peirce's law]]
 
{{col-break}}
 
{{col-break}}
 
* [[Propositional calculus]]
 
* [[Propositional calculus]]
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* [[Sole sufficient operator]]
 
* [[Truth table]]
 
* [[Truth table]]
 
* [[Universe of discourse]]
 
* [[Universe of discourse]]
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{{col-end}}
 
{{col-end}}
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==Document history==
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===Relational concepts===
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{{col-begin}}
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{{col-break}}
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* [[Continuous predicate]]
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* [[Hypostatic abstraction]]
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* [[Logic of relatives]]
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* [[Logical matrix]]
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{{col-break}}
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* [[Relation (mathematics)|Relation]]
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* [[Relation composition]]
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* [[Relation construction]]
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* [[Relation reduction]]
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{{col-break}}
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* [[Relation theory]]
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* [[Relative term]]
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* [[Sign relation]]
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* [[Triadic relation]]
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{{col-end}}
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===Information, Inquiry===
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{{col-begin}}
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{{col-break}}
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* [[Inquiry]]
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* [[Dynamics of inquiry]]
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{{col-break}}
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* [[Semeiotic]]
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* [[Logic of information]]
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{{col-break}}
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* [[Descriptive science]]
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* [[Normative science]]
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{{col-break}}
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* [[Pragmatic maxim]]
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* [[Truth theory]]
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{{col-end}}
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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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===Related articles===
    
{{col-begin}}
 
{{col-begin}}
 
{{col-break}}
 
{{col-break}}
* [http://mywikibiz.com/Logical_equality Logical Equality], [http://mywikibiz.com/ MyWikiBiz]
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* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
* [http://beta.wikiversity.org/wiki/Logical_equality Logical Equality], [http://beta.wikiversity.org/ Beta Wikiversity]
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* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
* [http://www.getwiki.net/-Logical_Equality Logical Equality], [http://www.getwiki.net/ GetWiki]
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* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
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{{col-break}}
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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://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
 
{{col-break}}
 
{{col-break}}
* [http://www.wikinfo.org/index.php/Logical_equality Logical Equality], [http://www.wikinfo.org/ Wikinfo]
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* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
* [http://www.textop.org/wiki/index.php?title=Logical_equality Logical Equality], [http://www.textop.org/wiki/ Textop Wiki]
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* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
* [http://en.wikipedia.org/w/index.php?title=Logical_equality&oldid=77110577 Logical Equality], [http://en.wikipedia.org/ Wikipedia]
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* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
 
{{col-end}}
 
{{col-end}}
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<br><sharethis />
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==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.
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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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* [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]
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* [http://beta.wikiversity.org/wiki/Logical_equality Logical Equality], [http://beta.wikiversity.org/ Wikiversity Beta]
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* [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]]
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[[Category:Open Educational Resource]]
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[[Category:Peer Educational Resource]]
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[[Category:Charles Sanders Peirce]]
 
[[Category:Computer Science]]
 
[[Category:Computer Science]]
 
[[Category:Formal Languages]]
 
[[Category:Formal Languages]]
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