Editing Necessity and sufficiency (section)

{{Short description|Terms to describe a conditional relationship between two statements}}
{{about|the formal terminology in logic|causal meanings of the terms|Causality|the concepts in statistics|Sufficient statistic}}
{{redirect|Necessary But Not Sufficient|the novel by Eliyahu Goldratt|Necessary But Not Sufficient (novel)}}
In [[logic]] and [[mathematics]], '''necessity''' and '''sufficiency''' are terms used to describe a [[material conditional|conditional]] or implicational relationship between two [[Statement (logic)|statements]]. For example, in the [[Conditional sentence|conditional statement]]: "If {{mvar|P}} then {{mvar|Q}}", {{mvar|Q}} is '''necessary''' for {{mvar|P}}, because the [[Truth value|truth]] of {{mvar|Q}} is guaranteed by the truth of {{mvar|P}}. (Equivalently, it is impossible to have {{mvar|P}} without {{mvar|Q}}, or the falsity of {{mvar|Q}} ensures the falsity of {{mvar|P}}.)<ref name=":0">{{Cite web|url=https://philosophy.hku.hk/think/meaning/nsc.php|title=[M06] Necessity and sufficiency|website=philosophy.hku.hk|access-date=2019-12-02}}</ref> Similarly, {{mvar|P}} is '''sufficient''' for {{mvar|Q}}, because {{mvar|P}} being true always implies that {{mvar|Q}} is true, but {{mvar|P}} not being true does not always imply that {{mvar|Q}} is not true.<ref>{{Cite book|title=Proofs and Fundamentals: A First Course in Abstract Mathematics|last=Bloch|first=Ethan D.|publisher=Springer|year=2011|isbn=978-1-4419-7126-5|pages=8–9}}</ref>

In general, a necessary condition is one (possibly one of several conditions) that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition.<ref>{{Cite web|url=https://www.txstate.edu/philosophy/resources/fallacy-definitions/Confusion-of-Necessary.html|title=Confusion of Necessary with a Sufficient Condition|last=Confusion-of-Necessary|date=2019-05-15|website=www.txstate.edu|language=en|access-date=2019-12-02}}</ref> The assertion that a statement is a "necessary ''and'' sufficient" condition of another means that the former statement is true [[if and only if]] the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false.<ref name=betz>{{cite book|last=Betz|first=Frederick|title=Managing Science: Methodology and Organization of Research|date=2011|publisher=Springer|location=New York|isbn=978-1-4419-7487-7|page=247}}</ref><ref name=Manktelow>{{cite book|last=Manktelow|first=K. I.|title=Reasoning and Thinking|date=1999|publisher=Psychology Press|location=East Sussex, UK|isbn=0-86377-708-2}}</ref><ref name=asnina>{{cite journal|author1=Asnina, Erika |author2=Osis, Janis |author3=Jansone, Asnate |name-list-style=amp |title=Formal Specification of Topological Relations|journal=Databases and Information Systems VII|date=2013|volume=249 |issue=Databases and Information Systems VII |page=175|doi=10.3233/978-1-61499-161-8-175}}</ref>

In [[ordinary English]] (also [[natural language]]) "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. For example, being round is a necessary condition for being a circle, but it is not sufficient since ovals and ellipses are round, but not circles — while being a circle is a sufficient condition for being round.
Any conditional statement consists of at least one sufficient condition and at least one necessary condition.

In [[Analytics|data analytics]], necessity and sufficiency can refer to different [[Causality|causal]] logics,<ref>{{Cite journal |last=Richter |first=Nicole Franziska |last2=Hauff |first2=Sven |date=2022-08-01 |title=Necessary conditions in international business research–Advancing the field with a new perspective on causality and data analysis |url=https://findresearcher.sdu.dk/ws/files/199180258/1_s2.0_S1090951622000037_main.pdf |journal=Journal of World Business |language=en |volume=57 |issue=5 |pages=101310 |doi=10.1016/j.jwb.2022.101310 |issn=1090-9516|doi-access=free }}</ref> where [[necessary condition analysis]] and [[qualitative comparative analysis]] can be used as analytical techniques for examining necessity and sufficiency of conditions for a particular outcome of interest.