Exclusive disjunction

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:

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

See also

Logical operators

Exclusive disjunction Logical conjunction Logical disjunction Logical equality

Logical implication Logical NAND Logical NNOR Negation

Related topics

Ampheck Boolean algebra Boolean domain Boolean function

Boolean logic Laws of Form Logic gate Logical graph

Peirce's law Propositional calculus Sole sufficient operator Zeroth order logic

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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