Difference between revisions of "Exclusive disjunction"
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==Syllabus== | ==Syllabus== | ||
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| + | ===Focal nodes=== | ||
| + | |||
| + | {{col-begin}} | ||
| + | {{col-break}} | ||
| + | * [[Inquiry Live]] | ||
| + | {{col-break}} | ||
| + | * [[Logic Live]] | ||
| + | {{col-end}} | ||
| + | |||
| + | ===Peer nodes=== | ||
| + | |||
| + | {{col-begin}} | ||
| + | {{col-break}} | ||
| + | * [http://mywikibiz.com/Exclusive_disjunction Exclusive Disjunction @ MyWikiBiz] | ||
| + | * [http://mathweb.org/wiki/Exclusive_disjunction Exclusive Disjunction @ MathWeb Wiki] | ||
| + | * [http://netknowledge.org/wiki/Exclusive_disjunction Exclusive Disjunction @ NetKnowledge] | ||
| + | {{col-break}} | ||
| + | * [http://wiki.oercommons.org/mediawiki/index.php/Exclusive_disjunction Exclusive Disjunction @ OER Commons] | ||
| + | * [http://p2pfoundation.net/Exclusive_Disjunction Exclusive Disjunction @ P2P Foundation] | ||
| + | * [http://semanticweb.org/wiki/Exclusive_disjunction Exclusive Disjunction @ SemanticWeb] | ||
| + | {{col-end}} | ||
===Logical operators=== | ===Logical operators=== | ||
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* [[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]] | ||
* [[Zeroth order logic]] | * [[Zeroth order logic]] | ||
{{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]] | ||
| + | * [[Logic of information]] | ||
| + | {{col-break}} | ||
| + | * [[Descriptive science]] | ||
| + | * [[Normative science]] | ||
| + | {{col-break}} | ||
| + | * [[Pragmatic maxim]] | ||
| + | * [[Pragmatic theory of truth]] | ||
| + | {{col-break}} | ||
| + | * [[Semeiotic]] | ||
| + | * [[Semiotic information]] | ||
| + | {{col-end}} | ||
| + | |||
| + | ===Related articles=== | ||
| + | |||
| + | * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, “Introduction To Inquiry Driven Systems”] | ||
| + | |||
| + | * [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, “Prospects For Inquiry Driven Systems”] | ||
| + | |||
| + | * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, “Inquiry Driven Systems : Inquiry Into Inquiry”] | ||
| + | |||
| + | * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, “Propositional Equation Reasoning Systems”] | ||
| + | |||
| + | * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, “Differential Logic : Introduction”] | ||
| + | |||
| + | * [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, “Differential Propositional Calculus”] | ||
| + | |||
| + | * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, “Differential Logic and Dynamic Systems”] | ||
==Document history== | ==Document history== | ||
Revision as of 18:05, 14 May 2010
Exclusive disjunction, also known as logical inequality or symmetric difference, is an operation on two logical values, typically the values of two propositions, that produces a value of true just in case exactly one of its operands is true.
The truth table of p XOR q (also written as p + q or p ≠ q) is as follows:
| p | q | p XOR q |
|---|---|---|
| F | F | F |
| F | T | T |
| T | F | T |
| T | T | F |
The following equivalents can then be deduced:
\[\begin{matrix} p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q) \\ \\ & = & (p \lor q) & \land & (\lnot p \lor \lnot q) \\ \\ & = & (p \lor q) & \land & \lnot (p \land q) \end{matrix}\]
Syllabus
Focal nodes
Template:Col-breakTemplate:Col-breakTemplate:Col-endPeer nodes
- Exclusive Disjunction @ MyWikiBiz
- Exclusive Disjunction @ MathWeb Wiki
- Exclusive Disjunction @ NetKnowledge
- Exclusive Disjunction @ OER Commons
- Exclusive Disjunction @ P2P Foundation
- Exclusive Disjunction @ SemanticWeb
Logical operators
Related topics
- Propositional calculus
- Sole sufficient operator
- Truth table
- Universe of discourse
- Zeroth order logic
Relational concepts
Information, Inquiry
Related articles
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.
- Exclusive Disjunction, MyWikiBiz
- Exclusive Disjunction, Beta Wikiversity
- Exclusive Disjunction, GetWiki
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