====== Contravalence ======
Refers to an //exclusive// [[glossary:disjunction|disjunction]] ("or"-statement). //Contravalence// can be paraphrased as "either A, //or// B, //but not both//".
For example:
> For dessert, you can have fruit salad //or// ice cream [//but not both//].
===== Description =====
A contravalence is a statement that is //true// if exactly one of the two sub-statements is //true//, i.e. in this case if there is fruit for dessert //or// if there is ice cream. Unlike in an [[glossary:adjunction|adjunction]] (inclusive disjunction), the overall expression is not //true// if both partial statements are //true//, i.e. if both, ice cream //and// fruit are served.
^ A ^ B ^ A ⊻ B ^
| true | true | false |
| true | false | true |
| false | true | true |
| false | false | false |
===== Colloquial use =====
Although there is no specific word for an exclusive "or" in English, people often try to clarify this meaning by constructions such as "either … or …", or by emphasizing: "… but not both". This is often awkward and does not exactly represent the meaning of the logical expression.
Occasionally, the neologism "xor" ("//exclusive or// "), originating from information sciences, is occasionally used in written language to denote a //contravalence//.
In Latin, the word "aut" stands for an exclusive "or". This term is also occasionally used to denote //contravalence//.
===== Logical symbol =====
On this website, the symbol ''⊻'' is used for contravalence. In other places, you may also find ''⊕'' or ''⩒'' instead. These symbols are all pronounced "aut ".
An alternative is the term "xor", as explained above (pronounced: "ex-or ").
===== See also =====
* [[glossary:disjunction|Disjunction]]
* [[glossary:adjunction|Adjunction]]
===== More information =====
* [[wp>Exclusive or]] on//Wikipedia//
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