Difference between revisions of "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. | '''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 <math>p ~\operatorname{XOR}~ q,</math> also written <math>p + q\!</math> or <math>p \ne q,\!</math> appears below: | + | The [[truth table]] of <math>p ~\operatorname{XOR}~ q,</math> also written <math>p + q~\!</math> or <math>p \ne q,\!</math> appears below: |
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Latest revision as of 01:45, 31 October 2015
☞ 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 \(p ~\operatorname{XOR}~ q,\) also written \(p + q~\!\) or \(p \ne q,\!\) appears below:
| \(p\!\) | \(q\!\) | \(p ~\operatorname{XOR}~ q\) |
| \(\operatorname{F}\) | \(\operatorname{F}\) | \(\operatorname{F}\) |
| \(\operatorname{F}\) | \(\operatorname{T}\) | \(\operatorname{T}\) |
| \(\operatorname{T}\) | \(\operatorname{F}\) | \(\operatorname{T}\) |
| \(\operatorname{T}\) | \(\operatorname{T}\) | \(\operatorname{F}\) |
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
Peer nodes
- Exclusive Disjunction @ InterSciWiki
- Exclusive Disjunction @ MyWikiBiz
- Exclusive Disjunction @ Subject Wikis
- Exclusive Disjunction @ Wikiversity
- Exclusive Disjunction @ Wikiversity Beta
Logical operators
Template:Col-breakTemplate:Col-breakTemplate:Col-endRelated topics
- Propositional calculus
- Sole sufficient operator
- Truth table
- Universe of discourse
- Zeroth order logic
Relational concepts
Information, Inquiry
Related articles
- 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
