Exclusive disjunction

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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 \ne 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}
==Syllabus==
===Focal nodes===
* Inquiry Live
* Logic Live
===Peer nodes===
* Exclusive Disjunction @ InterSciWiki
* Exclusive Disjunction @ MyWikiBiz
* Exclusive Disjunction @ Subject Wikis
* Exclusive Disjunction @ Wikiversity
* Exclusive Disjunction @ Wikiversity Beta
===Logical operators===
* Exclusive disjunction
* Logical conjunction
* Logical disjunction
* Logical equality
* Logical implication
* Logical NAND
* Logical NNOR
* Negation
===Related topics===
* Ampheck
* Boolean domain
* Boolean function
* Boolean-valued function
* Differential logic
* Logical graph
* Minimal negation operator
* Multigrade operator
* Parametric operator
* Peirce's law
* Propositional calculus
* Sole sufficient operator
* Truth table
* Universe of discourse
* Zeroth order logic
===Relational concepts===
* Continuous predicate
* Hypostatic abstraction
* Logic of relatives
* Logical matrix
* Relation
* Relation composition
* Relation construction
* Relation reduction
* Relation theory
* Relative term
* Sign relation
* Triadic relation
===Information, Inquiry===
* Inquiry
* Dynamics of inquiry
* Semeiotic
* Logic of information
* Descriptive science
* Normative science
* Pragmatic maxim
* Truth theory
===Related articles===
* Cactus Language
* Futures Of Logical Graphs
* Propositional Equation Reasoning Systems
* 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.
* Exclusive Disjunction, InterSciWiki
* Exclusive Disjunction, MyWikiBiz
* Exclusive Disjunction, Subject Wikis
* Exclusive Disjunction, Wikinfo
* Exclusive Disjunction, Wikiversity
* Exclusive Disjunction, Wikiversity Beta
* Exclusive Disjunction, Wikipedia
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