"XOR" redirects here. For the logic gate, see XOR gate. For other uses, see XOR (disambiguation).
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Exclusive or
XOR
Truth table
Logic gate
Normal forms
Disjunctive
Conjunctive
Zhegalkin polynomial
Post's lattices
0-preserving
yes
1-preserving
no
Monotone
no
Affine
yes
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Logical connectives
AND
, , , ,
equivalent
, ,
implies
, ,
NAND
, , ,
nonequivalent
, ,
NOR
, ,
NOT
, , ,
OR
, , ,
XNOR
XOR
,
converse
, ,
Related concepts
Propositional calculus
Predicate logic
Boolean algebra
Truth table
Truth function
Boolean function
Functional completeness
Applications
Digital logic
Programming languages
Mathematical logic
Philosophy of logic
Category
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Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd.[1]
It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true. XOR excludes that case. Some informal ways of describing XOR are "one or the other but not both", "either one or the other", and "A or B, but not A and B".
It is symbolized by the prefix operator [2]: 16 and by the infix operators XOR (/ˌɛksˈɔːr/, /ˌɛksˈɔː/, /ˈksɔːr/ or /ˈksɔː/), EOR, EXOR, , , , ⩛, , , and .
^Bocheński, J. M. (1949). Précis de logique mathématique(PDF) (in French). The Netherlands: F. G. Kroonder, Bussum, Pays-Bas. Translated as Bocheński, J. M. (1959). A Precis of Mathematical Logic. Translated by Bird, O. Dordrecht, Holland: D. Reidel Publishing Company. doi:10.1007/978-94-017-0592-9. ISBN 978-90-481-8329-6.
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