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Logical disjunction is not disjunctive |
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In [[logic]] and [[mathematics]], a '''disjunction''' is an "or statement". For example "John skis or Sally swims" is a disjunction.
Note that in everyday language, use of the word "or" can sometimes mean "either, but not both" (eg, "would you like tea or coffee?"). In logic, this is called an [[Exclusive disjunction|"exclusive disjunction"]] or "exclusive or". When used formally, "or" allows for both parts of the or statement (its ''disjuncts'') to be true ("and/or"), therefore "or" is also called ''inclusive disjunction''. <small>''Note'': [[Boole]], closely following analogy with ordinary mathematics, premised, as a necessary condition to the definition of "x + y", that x and y were mutually exclusive. [[Jevons]], and practically all mathematical logicians after him, advocated, on various grounds, the definition of "logical addition" in a form which does not necessitate mutual exclusiveness.</small>
The statement "''P'' or ''Q''" is often written as
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