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 $p\text{XOR}q$ , also written $p+q$ or $p\ne q$ appears below:

$\text{Exclusive Disjunction}$

$p$	$q$	$p\text{XOR}q$
$\text{F}$	$\text{F}$	$\text{F}$
$\text{F}$	$\text{T}$	$\text{T}$
$\text{T}$	$\text{F}$	$\text{T}$
$\text{T}$	$\text{T}$	$\text{F}$

The following equivalents may then be deduced:

$\begin{array}{ccccc}p+q& =& (p\wedge \mathrm{\neg }q)& \vee & (\mathrm{\neg }p\wedge q)\\ [6pt]& =& (p\vee q)& \wedge & (\mathrm{\neg }p\vee \mathrm{\neg }q)\\ [6pt]& =& (p\vee q)& \wedge & \mathrm{\neg }(p\wedge q)\end{array}$

Syllabus

Focal nodes

• Inquiry Live
• Logic Live

Peer nodes

• Exclusive Disjunction @ InterSciWiki
• 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, Subject Wikis
• Exclusive Disjunction, Wikinfo
• Exclusive Disjunction, Wikiversity
• Exclusive Disjunction, Wikiversity Beta
• Exclusive Disjunction, Wikipedia