Exclusive disjunction: Difference between revisions

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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 $p~\operatorname {XOR} ~q,$ also written $p+q\!$ or $p\neq q,\!$ appears below:

${\text{Exclusive Disjunction}}\!$
$p\!$	$q\!$	$p~\operatorname {XOR} ~q$
$\operatorname {F}$	$\operatorname {F}$	$\operatorname {F}$
$\operatorname {F}$	$\operatorname {T}$	$\operatorname {T}$
$\operatorname {T}$	$\operatorname {F}$	$\operatorname {T}$
$\operatorname {T}$	$\operatorname {T}$	$\operatorname {F}$

The following equivalents may then be deduced:

${\begin{matrix}p+q&=&(p\land \lnot q)&\lor &(\lnot p\land q)\\[6pt]&=&(p\lor q)&\land &(\lnot p\lor \lnot q)\\[6pt]&=&(p\lor q)&\land &\lnot (p\land q)\end{matrix}}$

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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 @ MyWikiBiz]
 * [http://ref.subwiki.org/wiki/Exclusive_disjunction Exclusive Disjunction @ Subject Wikis]
-* [https://en.wikiversity.org/wiki/Exclusive_disjunction Exclusive Disjunction @ Wikiversity]
+* [http://en.wikiversity.org/wiki/Exclusive_disjunction Exclusive Disjunction @ Wikiversity]
-* [https://beta.wikiversity.org/wiki/Exclusive_disjunction Exclusive Disjunction @ Wikiversity Beta]
+* [http://beta.wikiversity.org/wiki/Exclusive_disjunction Exclusive Disjunction @ Wikiversity Beta]
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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://intersci.ss.uci.edu/wiki/index.php/Exclusive_disjunction Exclusive Disjunction], [http://intersci.ss.uci.edu/ InterSciWiki]
 * [http://mywikibiz.com/Exclusive_disjunction Exclusive Disjunction], [http://mywikibiz.com/ MyWikiBiz]
 * [http://ref.subwiki.org/wiki/Exclusive_disjunction Exclusive Disjunction], [http://ref.subwiki.org/ Subject Wikis]
-{{col-break}}
+* [http://wikinfo.org/w/index.php/Exclusive_disjunction Exclusive Disjunction], [http://wikinfo.org/w/ Wikinfo]
-* [http://wikinfo.org/index.php/Exclusive_disjunction Exclusive Disjunction], [http://wikinfo.org/ Wikinfo]
 * [http://en.wikiversity.org/wiki/Exclusive_disjunction Exclusive Disjunction], [http://en.wikiversity.org/ Wikiversity]
 * [http://beta.wikiversity.org/wiki/Exclusive_disjunction Exclusive Disjunction], [http://beta.wikiversity.org/ Wikiversity Beta]
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 * [http://en.wikipedia.org/w/index.php?title=Exclusive_disjunction&oldid=75153068 Exclusive Disjunction], [http://en.wikipedia.org/ Wikipedia]
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 [[Category:Inquiry]]