Difference between revisions of "Exclusive disjunction"
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==See also== | ==See also== | ||
===Logical operators=== | ===Logical operators=== | ||
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* [[Exclusive disjunction]] | * [[Exclusive disjunction]] | ||
* [[Logical conjunction]] | * [[Logical conjunction]] | ||
* [[Logical disjunction]] | * [[Logical disjunction]] | ||
* [[Logical equality]] | * [[Logical equality]] | ||
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* [[Logical implication]] | * [[Logical implication]] | ||
* [[Logical NAND]] | * [[Logical NAND]] | ||
* [[Logical NNOR]] | * [[Logical NNOR]] | ||
* [[Logical negation|Negation]] | * [[Logical negation|Negation]] | ||
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===Related topics=== | ===Related topics=== | ||
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* [[Ampheck]] | * [[Ampheck]] | ||
* [[Boolean algebra]] | * [[Boolean algebra]] | ||
* [[Boolean domain]] | * [[Boolean domain]] | ||
* [[Boolean function]] | * [[Boolean function]] | ||
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* [[Boolean logic]] | * [[Boolean logic]] | ||
* [[Laws of Form]] | * [[Laws of Form]] | ||
* [[Logic gate]] | * [[Logic gate]] | ||
* [[Logical graph]] | * [[Logical graph]] | ||
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* [[Peirce's law]] | * [[Peirce's law]] | ||
* [[Propositional calculus]] | * [[Propositional calculus]] | ||
* [[Sole sufficient operator]] | * [[Sole sufficient operator]] | ||
* [[Zeroth order logic]] | * [[Zeroth order logic]] | ||
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| − | + | <sharethis /> | |
[[Category:Computer Science]] | [[Category:Computer Science]] | ||
Revision as of 05:40, 25 May 2009
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 XOR q |
|---|---|---|
| F | F | F |
| F | T | T |
| T | F | T |
| T | T | F |
The following equivalents can then be deduced:
\[\begin{matrix} p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q) \\ \\ & = & (p \lor q) & \land & (\lnot p \lor \lnot q) \\ \\ & = & (p \lor q) & \land & \lnot (p \land q) \end{matrix}\]
