Difference between revisions of "Exclusive disjunction"
MyWikiBiz, Author Your Legacy — Saturday November 23, 2024
Jump to navigationJump to searchJon Awbrey (talk | contribs) (apply column template) |
Jon Awbrey (talk | contribs) |
||
| Line 31: | Line 31: | ||
==See also== | ==See also== | ||
| + | |||
===Logical operators=== | ===Logical operators=== | ||
Revision as of 14:08, 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:
\[\begin{matrix} p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q) \\ \\ & = & (p \lor q) & \land & (\lnot p \lor \lnot q) \\ \\ & = & (p \lor q) & \land & \lnot (p \land q) \end{matrix}\]
