Mutual exclusivity
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| - | '''Pigeonholing''' is any process that attempts to [[classification|classify]] [[disparate]] [[entity|entities]] into a small number of [[Category|categories]] (usually, [[Mutual exclusivity|mutually exclusive]] ones). | + | In [[logic]] and [[probability theory]], two propositions (or events) are '''mutually exclusive''' or '''disjoint''' if they cannot both be true (occur). A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both. |
| - | The term usually carries connotations of criticism, implying that the classification scheme referred to inadequately reflects the entities being sorted, or that it is based on [[stereotype]]s. | + | In the coin-tossing example, both outcomes are, in theory, [[Collectively exhaustive events|collectively exhaustive]], which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities. However, not all mutually exclusive events are collectively exhaustive. For example, the outcomes 1 and 4 of a single roll of a [[six-sided die]] are mutually exclusive (both cannot happen at the same time) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6). |
| - | Common failings of pigeonholing schemes include: | ||
| - | |||
| - | *Categories are poorly defined (often because they are [[Subjectivity|subjective]]). | ||
| - | *Entities may be suited to more than one category. Example: [[rhubarb]] is both 'poisonous' and 'edible'. | ||
| - | *Entities may not fit into any available category. Example: asking somebody from [[Washington, DC]] which state they live in. | ||
| - | *Entities may change over time, so they no longer fit the category in which they have been placed. Example: certain species of [[fish]] may change from male to female during their life. | ||
| - | *Attempting to discretize properties that would be better viewed as a [[continuum (theory)|continuum]]. Example: attempting to sort people into '[[Extraversion and introversion|introverted]]' and '[[Extraversion and introversion|extroverted]]'. | ||
| - | *Criteria used to categorize entities do not accurately predict the properties ascribed to those categories. Example: relying on [[astrological sign]] as a guide to someone's personality. | ||
| ==See also== | ==See also== | ||
| - | * [[Archetype]] | + | * [[Contrariety]] |
| - | * [[Labelling]] | + | * [[Dichotomy]] |
| - | * [[Pigeonhole principle]] | + | * [[Disjoint sets]] |
| - | * [[Typecasting (acting)]] | + | * [[Double bind]] |
| + | * [[Event structure]] | ||
| + | * [[Oxymoron]] | ||
| + | * [[Synchronicity]] | ||
| {{GFDL}} | {{GFDL}} | ||
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In logic and probability theory, two propositions (or events) are mutually exclusive or disjoint if they cannot both be true (occur). A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.
In the coin-tossing example, both outcomes are, in theory, collectively exhaustive, which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities. However, not all mutually exclusive events are collectively exhaustive. For example, the outcomes 1 and 4 of a single roll of a six-sided die are mutually exclusive (both cannot happen at the same time) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6).
See also
Unless indicated otherwise, the text in this article is either based on Wikipedia article "Mutual exclusivity" or another language Wikipedia page thereof used under the terms of the GNU Free Documentation License; or on research by Jahsonic and friends. See Art and Popular Culture's copyright notice.
