Difference between revisions of "Exclusive disjunction"
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'''Exclusive disjunction''', also known as '''logical inequality''' or '''symmetric difference''', is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, 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 [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, 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''' | + | The [[truth table]] of '''p XOR q''' (also written as '''p + q''' or '''p ≠ q''') is as follows: |
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:45%" | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:45%" | ||
Revision as of 02:50, 3 April 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:
\[\begin{matrix} p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q) \\ \\ & = & (p \lor q) & \land & (\lnot p \lor \lnot q) \\ \\ & = & (p \lor q) & \land & \lnot (p \land q) \end{matrix}\]
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.
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