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Exclusive disjunction

MyWikiBiz, Author Your Legacy — Thursday August 07, 2008

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:

**Exclusive Disjunction**
p	q	p XOR q
F	F	F
F	T	T
T	F	T
T	T	F

The following equivalents can then be deduced:

$\begin{matrix} p + q & = & (p \land \lnot q) & \lor & (\lnot p \land q) \\ \\ & = & (p \lor q) & \land & (\lnot p \lor \lnot q) \\ \\ & = & (p \lor q) & \land & \lnot (p \land q) \end{matrix}$

1 See also
- 1.1 Logical operators
- 1.2 Related topics
2 Aficionados

[edit] See also

[edit] Logical operators

[edit] Related topics

[edit] Aficionados

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