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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.
| + | <font size="3">☞</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 ↔ q''', or '''p ≡ q''') is as follows:
| + | '''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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− | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:45%" | + | 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: |
− | |+ '''Logical Equality''' | + | |
− | |- style="background:paleturquoise" | + | <br> |
− | ! style="width:15%" | p
| + | |
− | ! style="width:15%" | q
| + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:45%" |
− | ! style="width:15%" | p = q
| + | |+ style="height:30px" | <math>\text{Logical Equality}\!</math> |
| + | |- 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> |
| |} | | |} |
| + | |
| <br> | | <br> |
| | | |
− | ==See also== | + | ==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=== |
− | {| | + | |
− | | valign=top |
| + | {{col-begin}} |
| + | {{col-break}} |
| * [[Exclusive disjunction]] | | * [[Exclusive disjunction]] |
| * [[Logical conjunction]] | | * [[Logical conjunction]] |
| * [[Logical disjunction]] | | * [[Logical disjunction]] |
| * [[Logical equality]] | | * [[Logical equality]] |
− | | valign=top |
| + | {{col-break}} |
| * [[Logical implication]] | | * [[Logical implication]] |
| * [[Logical NAND]] | | * [[Logical NAND]] |
| * [[Logical NNOR]] | | * [[Logical NNOR]] |
| * [[Logical negation|Negation]] | | * [[Logical negation|Negation]] |
− | |}
| + | {{col-end}} |
| + | |
| ===Related topics=== | | ===Related topics=== |
− | {| | + | |
− | | valign=top |
| + | {{col-begin}} |
| + | {{col-break}} |
| * [[Ampheck]] | | * [[Ampheck]] |
− | * [[Boolean algebra]]
| |
| * [[Boolean domain]] | | * [[Boolean domain]] |
| * [[Boolean function]] | | * [[Boolean function]] |
− | | valign=top |
| + | * [[Boolean-valued function]] |
− | * [[Boolean logic]] | + | * [[Differential logic]] |
− | * [[Laws of Form]] | + | {{col-break}} |
− | * [[Logic gate]]
| |
| * [[Logical graph]] | | * [[Logical graph]] |
− | | valign=top |
| + | * [[Minimal negation operator]] |
| + | * [[Multigrade operator]] |
| + | * [[Parametric operator]] |
| * [[Peirce's law]] | | * [[Peirce's law]] |
| + | {{col-break}} |
| * [[Propositional calculus]] | | * [[Propositional calculus]] |
| * [[Sole sufficient operator]] | | * [[Sole sufficient operator]] |
| + | * [[Truth table]] |
| + | * [[Universe of discourse]] |
| * [[Zeroth order logic]] | | * [[Zeroth order logic]] |
− | |} | + | {{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-break}} |
| + | * [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://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}} |
| + | * [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://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry] |
| + | {{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. |
| | | |
− | {{aficionados}}<sharethis />
| + | * [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]] |