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> | + | The [[truth table]] of <math>p ~\operatorname{XOR}~ q,</math> also written as <math>p + q\!</math> or <math>p \ne q,\!</math> is shown below: |
<br> | <br> | ||
Revision as of 11:12, 15 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 \(p ~\operatorname{XOR}~ q,\) also written as \(p + q\!\) or \(p \ne q,\!\) is shown 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:
|
\(\begin{matrix} p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q) \\[6pt] & = & (p \lor q) & \land & (\lnot p \lor \lnot q) \\[6pt] & = & (p \lor q) & \land & \lnot (p \land q) \end{matrix}\) |
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- Exclusive Disjunction @ MyWikiBiz
- Exclusive Disjunction @ InterSciWiki
- Exclusive Disjunction @ OER Commons
- Exclusive Disjunction @ P2P Foundation
- Exclusive Disjunction @ Subject Wikis
- Exclusive Disjunction @ Wikiversity Beta
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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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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