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exclusive or (Definition)

The logical operator xor, short for “exclusive or”, is a binary operator that is true iff exactly one of its parameters is true, and thus corresponds to the normal use of “or” in English. Xor uses the symbol $\oplus$ due to its similarity to disjunction, which sometimes uses $+$. The truth table for xor is

$a$ $b$ $a \oplus b$
F F F
F T T
T F T
T T F



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See Also: disjunction, propositional logic

Other names:  xor, logical xor, logical exclusive or
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Cross-references: truth table, disjunction, parameters, iff, binary, operator
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This is version 3 of exclusive or, born on 2008-05-25, modified 2008-05-25.
Object id is 10620, canonical name is ExclusiveOr.
Accessed 602 times total.

Classification:
AMS MSC03B05 (Mathematical logic and foundations :: General logic :: Classical propositional logic)

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