Difference between revisions of "Exclusive disjunction"
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* [[Logical graph]] | * [[Logical graph]] | ||
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| + | * [[Minimal negation operator]] | ||
| + | * [[Peirce's law]] | ||
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* [[Propositional calculus]] | * [[Propositional calculus]] | ||
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* [[Zeroth order logic]] | * [[Zeroth order logic]] | ||
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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://mywikibiz.com/Exclusive_disjunction Exclusive Disjunction], [http://mywikibiz.com/ MyWikiBiz] | ||
| + | * [http://beta.wikiversity.org/wiki/Exclusive_disjunction Exclusive Disjunction], [http://beta.wikiversity.org/ Beta Wikiversity] | ||
| + | * [http://www.getwiki.net/-Exclusive_disjunction Exclusive Disjunction], [http://www.getwiki.net/ GetWiki] | ||
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| + | * [http://www.wikinfo.org/index.php/Exclusive_disjunction Exclusive Disjunction], [http://www.wikinfo.org/ Wikinfo] | ||
| + | * [http://www.textop.org/wiki/index.php?title=Exclusive_disjunction Exclusive Disjunction], [http://www.textop.org/wiki/ Textop Wiki] | ||
| + | * [http://en.wikipedia.org/w/index.php?title=Exclusive_disjunction Exclusive Disjunction], [http://en.wikipedia.org/ Wikipedia] | ||
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Revision as of 01:18, 6 April 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
Logical operators
Template:Col-breakTemplate:Col-breakTemplate:Col-endRelated topics
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
<sharethis />
