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 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:
\[\begin{matrix} p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q) \\ \\ & = & (p \lor q) & \land & (\lnot p \lor \lnot q) \\ \\ & = & (p \lor q) & \land & \lnot (p \land q) \end{matrix}\]
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- 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
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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
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- Exclusive Disjunction, GetWiki
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