Difference between revisions of "Logical equality"
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<font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. | <font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]]. | ||
− | '''Logical equality''' is an | + | '''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 | + | 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> | ||
− | {| align="center" border="1" cellpadding="8" cellspacing="0" style=" | + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%" |
− | |+ | + | |+ style="height:30px" | <math>\text{Logical Equality}\!</math> |
− | |- style="background:# | + | |- style="height:40px; background:#f0f0ff" |
− | + | | style="width:33%" | <math>p\!</math> | |
− | + | | style="width:33%" | <math>q\!</math> | |
− | + | | style="width:33%" | <math>p = q\!</math> | |
|- | |- | ||
− | | F || F || T | + | | <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math> |
|- | |- | ||
− | | F || T || F | + | | <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math> |
|- | |- | ||
− | | T || F || F | + | | <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math> |
|- | |- | ||
− | | T || T || T | + | | <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=== | ||
− | + | * [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] | ||
− | * [http:// | + | * [http://ref.subwiki.org/wiki/Logical_equality Logical Equality @ Subject Wikis] |
− | + | * [http://en.wikiversity.org/wiki/Logical_equality Logical Equality @ Wikiversity] | |
− | + | * [http://beta.wikiversity.org/wiki/Logical_equality Logical Equality @ Wikiversity Beta] | |
− | * [http:// | ||
− | * [http:// | ||
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===Logical operators=== | ===Logical operators=== | ||
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{{col-break}} | {{col-break}} | ||
* [[Inquiry]] | * [[Inquiry]] | ||
+ | * [[Dynamics of inquiry]] | ||
+ | {{col-break}} | ||
+ | * [[Semeiotic]] | ||
* [[Logic of information]] | * [[Logic of information]] | ||
{{col-break}} | {{col-break}} | ||
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{{col-break}} | {{col-break}} | ||
* [[Pragmatic maxim]] | * [[Pragmatic maxim]] | ||
− | * [[ | + | * [[Truth theory]] |
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{{col-end}} | {{col-end}} | ||
===Related articles=== | ===Related articles=== | ||
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− | * [http:// | + | * [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language] |
− | + | * [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs] | |
− | * [http:// | + | * [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems] |
− | + | {{col-break}} | |
− | * [http:// | + | * [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction] |
− | + | * [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus] | |
− | * [http:// | + | * [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems] |
− | + | {{col-break}} | |
− | * [http:// | + | * [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems] |
− | + | * [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems] | |
− | * [http:// | + | * [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry] |
+ | {{col-end}} | ||
==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. | ||
− | + | * [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] | * [http://mywikibiz.com/Logical_equality Logical Equality], [http://mywikibiz.com/ MyWikiBiz] | ||
+ | * [http://wikinfo.org/w/index.php/Logical_equality Logical Equality], [http://wikinfo.org/w/ Wikinfo] | ||
+ | * [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://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]] | ||
+ | [[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:
\(p\!\) | \(q\!\) | \(p = q\!\) |
\(\operatorname{F}\) | \(\operatorname{F}\) | \(\operatorname{T}\) |
\(\operatorname{F}\) | \(\operatorname{T}\) | \(\operatorname{F}\) |
\(\operatorname{T}\) | \(\operatorname{F}\) | \(\operatorname{F}\) |
\(\operatorname{T}\) | \(\operatorname{T}\) | \(\operatorname{T}\) |
Syllabus
Focal nodes
Peer nodes
- Logical Equality @ InterSciWiki
- Logical Equality @ MyWikiBiz
- Logical Equality @ Subject Wikis
- Logical Equality @ Wikiversity
- Logical Equality @ Wikiversity Beta
Logical operators
Template:Col-breakTemplate:Col-breakTemplate:Col-endRelated topics
- Propositional calculus
- Sole sufficient operator
- Truth table
- Universe of discourse
- Zeroth order logic
Relational concepts
Information, Inquiry
Related articles
- Differential Logic : Introduction
- Differential Propositional Calculus
- Differential Logic and Dynamic Systems
- Prospects for Inquiry Driven Systems
- Introduction to Inquiry Driven Systems
- Inquiry Driven Systems : Inquiry Into Inquiry
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.
- Logical Equality, InterSciWiki
- Logical Equality, MyWikiBiz
- Logical Equality, Wikinfo
- Logical Equality, Wikiversity
- Logical Equality, Wikiversity Beta
- Logical Equality, Wikipedia