Difference between revisions of "Exclusive disjunction"
MyWikiBiz, Author Your Legacy — Tuesday December 03, 2024
Jump to navigationJump to searchJon Awbrey (talk | contribs) (add cats) |
Jon Awbrey (talk | contribs) (add cats) |
||
| Line 66: | Line 66: | ||
[[Category:Computer Science]] | [[Category:Computer Science]] | ||
| + | [[Category:Formal Languages]] | ||
| + | [[Category:Formal Sciences]] | ||
| + | [[Category:Formal Systems]] | ||
[[Category:Linguistics]] | [[Category:Linguistics]] | ||
[[Category:Logic]] | [[Category:Logic]] | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
| + | [[Category:Philosophy]] | ||
[[Category:Semiotics]] | [[Category:Semiotics]] | ||
| − | |||
Revision as of 14:33, 21 May 2007
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, 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:
\[\begin{matrix} p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q) \\ \\ & = & (p \lor q) & \land & (\lnot p \lor \lnot q) \\ \\ & = & (p \lor q) & \land & \lnot (p \land q) \end{matrix}\]
See also
Logical operators
Related topics
Aficionados
- See Talk:Exclusive disjunction for discussions/comments regarding this article.
- See Exclusive disjunction/Aficionados for those who have listed Exclusive disjunction as an interest.
- See Talk:Exclusive disjunction/Aficionados for discussions regarding this interest.
<sharethis />
