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]]. | |
− | The [[truth table]] of | + | '''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 <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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==Syllabus== | ==Syllabus== | ||
+ | |||
+ | ===Focal nodes=== | ||
+ | |||
+ | * [[Inquiry Live]] | ||
+ | * [[Logic Live]] | ||
+ | |||
+ | ===Peer nodes=== | ||
+ | |||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Logical_equality Logical Equality @ InterSciWiki] | ||
+ | * [http://mywikibiz.com/Logical_equality Logical Equality @ MyWikiBiz] | ||
+ | * [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] | ||
===Logical operators=== | ===Logical operators=== | ||
Line 48: | Line 63: | ||
* [[Boolean function]] | * [[Boolean function]] | ||
* [[Boolean-valued function]] | * [[Boolean-valued function]] | ||
+ | * [[Differential logic]] | ||
{{col-break}} | {{col-break}} | ||
* [[Logical graph]] | * [[Logical graph]] | ||
− | |||
* [[Minimal negation operator]] | * [[Minimal negation operator]] | ||
+ | * [[Multigrade operator]] | ||
+ | * [[Parametric operator]] | ||
* [[Peirce's law]] | * [[Peirce's law]] | ||
{{col-break}} | {{col-break}} | ||
* [[Propositional calculus]] | * [[Propositional calculus]] | ||
+ | * [[Sole sufficient operator]] | ||
* [[Truth table]] | * [[Truth table]] | ||
* [[Universe of discourse]] | * [[Universe of discourse]] | ||
Line 60: | Line 78: | ||
{{col-end}} | {{col-end}} | ||
− | == | + | ===Relational concepts=== |
+ | |||
+ | {{col-begin}} | ||
+ | {{col-break}} | ||
+ | * [[Continuous predicate]] | ||
+ | * [[Hypostatic abstraction]] | ||
+ | * [[Logic of relatives]] | ||
+ | * [[Logical matrix]] | ||
+ | {{col-break}} | ||
+ | * [[Relation (mathematics)|Relation]] | ||
+ | * [[Relation composition]] | ||
+ | * [[Relation construction]] | ||
+ | * [[Relation reduction]] | ||
+ | {{col-break}} | ||
+ | * [[Relation theory]] | ||
+ | * [[Relative term]] | ||
+ | * [[Sign relation]] | ||
+ | * [[Triadic relation]] | ||
+ | {{col-end}} | ||
+ | |||
+ | ===Information, Inquiry=== | ||
+ | |||
+ | {{col-begin}} | ||
+ | {{col-break}} | ||
+ | * [[Inquiry]] | ||
+ | * [[Dynamics of inquiry]] | ||
+ | {{col-break}} | ||
+ | * [[Semeiotic]] | ||
+ | * [[Logic of information]] | ||
+ | {{col-break}} | ||
+ | * [[Descriptive science]] | ||
+ | * [[Normative science]] | ||
+ | {{col-break}} | ||
+ | * [[Pragmatic maxim]] | ||
+ | * [[Truth theory]] | ||
+ | {{col-end}} | ||
− | + | ===Related articles=== | |
{{col-begin}} | {{col-begin}} | ||
{{col-break}} | {{col-break}} | ||
− | * [http:// | + | * [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language] |
− | * [http:// | + | * [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://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://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems] | ||
{{col-break}} | {{col-break}} | ||
− | * [http:// | + | * [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems] |
− | * [http:// | + | * [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}} | {{col-end}} | ||
− | + | ==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. | ||
+ | |||
+ | * [http://intersci.ss.uci.edu/wiki/index.php/Logical_equality Logical Equality], [http://intersci.ss.uci.edu/ InterSciWiki] | ||
+ | * [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://en.wikipedia.org/w/index.php?title=Logical_equality&oldid=77110577 Logical Equality], [http://en.wikipedia.org/ Wikipedia] | ||
+ | [[Category:Inquiry]] | ||
+ | [[Category:Open 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