====== Adjunction (logic) ======

Denotes an //inclusive// [[glossary:disjunction|disjunction]] (“or”). Adjunction can be para­phrased as "either A, or B, //or both//".

For example:

> Today there is going to be fog, or rain [or both].

An //adjunction// is true when //at least// one of the two sub-expressions is //true//, that is, when it is raining or when there is fog. Unlike with [[glossary:contravalence|contra­valences]] (//exclusive// disjunctions), an ad­junction also evalu­ates to //true//, if //both// sub-expressions are //true// – that is, if it is //both// foggy and raining.

===== Other names =====

  * Inclusive “or”

===== Truth table =====

<aside float-right>
<figure>
{{ :logic:glossary:adjunction.svg|Adjunction Venn-diagram}}
<figcaption>Venn-diagram: adjunction <span "A vel B">A ∨ B</span></figcaption>
</figure>
</aside>
An //adjunction// is true if at least one of the sub-statements is true.

^ A ^ B ^ <span "A vel B">A ∨ B</span> ^
| true | true | true |
| true | false | true |
| false | true | true |
| false | false | false |

===== Colloquial use =====

In many languages – including English – no distinction is made between //in//clusive and //ex//clusive "or". Unless it is indicated otherwise, normal colloquial use of the word should assume an inclusive meaning (i.e., an //adjunction//), since this is by far the most common usage.

In Latin, however, there are explicitly different expressions for the two disjunctions, with the word <i :la "Lat.: or (inclusive)">vel</i> standing for an inclusive "or".

===== Logical symbol =====

In the context of this website, the <span "vel">∨</span> symbol (pronounced: "<em :la>vel</em> ") is used as a sign for inclusive disjunction. In other publications, symbols like <span "Plus">+</span>, or <span "Parallelen">∥</span>, or others are used with the same meaning.

===== See also =====

  * [[glossary:disjunction|Disjunction]]
  * [[glossary:contravalence|Contravalence]]

===== More Information =====

  * [[wp>Logical disjunction]] on //Wikipedia//

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