Difference between revisions of "Exclusive disjunction"
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| − | |+ | + | |+ style="height:30px" | <math>\text{Exclusive Disjunction}\!</math> |
| − | |- style="background:# | + | |- style="height:40px; background:#f0f0ff" |
| − | + | | style="width:33%" | <math>p\!</math> | |
| − | + | | style="width:33%" | <math>q\!</math> | |
| − | + | | style="width:33%" | <math>p ~\operatorname{XOR}~ q</math> | |
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| − | | F || F || F | + | | <math>\operatorname{F}</math> || <math>\operatorname{F}</math> || <math>\operatorname{F}</math> |
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| − | | F || T || T | + | | <math>\operatorname{F}</math> || <math>\operatorname{T}</math> || <math>\operatorname{T}</math> |
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| − | | T || F || T | + | | <math>\operatorname{T}</math> || <math>\operatorname{F}</math> || <math>\operatorname{T}</math> |
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| − | | T || T || F | + | | <math>\operatorname{T}</math> || <math>\operatorname{T}</math> || <math>\operatorname{F}</math> |
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Revision as of 15:50, 13 May 2012
☞ This page belongs to resource collections on Logic and Inquiry.
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:
| \(p\!\) | \(q\!\) | \(p ~\operatorname{XOR}~ q\) |
| \(\operatorname{F}\) | \(\operatorname{F}\) | \(\operatorname{F}\) |
| \(\operatorname{F}\) | \(\operatorname{T}\) | \(\operatorname{T}\) |
| \(\operatorname{T}\) | \(\operatorname{F}\) | \(\operatorname{T}\) |
| \(\operatorname{T}\) | \(\operatorname{T}\) | \(\operatorname{F}\) |
The following equivalents 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
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- 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
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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, Wikiversity Beta
- Exclusive Disjunction, GetWiki
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