翻訳と辞書
Words near each other
・ "O" Is for Outlaw
・ "O"-Jung.Ban.Hap.
・ "Ode-to-Napoleon" hexachord
・ "Oh Yeah!" Live
・ "Our Contemporary" regional art exhibition (Leningrad, 1975)
・ "P" Is for Peril
・ "Pimpernel" Smith
・ "Polish death camp" controversy
・ "Pro knigi" ("About books")
・ "Prosopa" Greek Television Awards
・ "Pussy Cats" Starring the Walkmen
・ "Q" Is for Quarry
・ "R" Is for Ricochet
・ "R" The King (2016 film)
・ "Rags" Ragland
・ ! (album)
・ ! (disambiguation)
・ !!
・ !!!
・ !!! (album)
・ !!Destroy-Oh-Boy!!
・ !Action Pact!
・ !Arriba! La Pachanga
・ !Hero
・ !Hero (album)
・ !Kung language
・ !Oka Tokat
・ !PAUS3
・ !T.O.O.H.!
・ !Women Art Revolution


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Necessary condition : ウィキペディア英語版
Necessity and sufficiency

In logic, necessity and sufficiency are implicational relationships between statements. The assertion that one 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.
In ordinary English, 'necessary' and 'sufficient' indicate relations between conditions or states of affairs, not statements. Being a male sibling is a necessary and sufficient condition for being a brother. Fred's being a male sibling is necessary and sufficient for the truth of the statement that Fred is a brother.
==Definitions==

A true ''necessary'' condition in a conditional statement makes the statement true (see "truth table" immediately below). In formal terms, a consequent ''N'' is a necessary condition for an antecedent ''S'', in the conditional statement, "''N'' if ''S'' ", "''N'' is implied by ''S'' ", or . In common words, we would also say "''N'' is weaker than ''S'' " or "''S'' cannot occur without ''N'' ". For example, it is necessary to be Named, to be called "Socrates".
A true ''sufficient'' condition in a conditional statement ties the statement's truth to its consequent. In formal terms, an antecedent ''S'' is a sufficient condition for a consequent ''N'', in the conditional statement, "if ''S'', then ''N'' ", "''S'' implies ''N'' ", or . In common words, we would also say "''S'' is stronger than ''N'' " or "''S'' guarantees ''N'' ". For example, "Socrates" suffices for a Name.
A ''necessary and sufficient'' condition requires both of these implications ( and ) to hold. Using the previous statement, this is expressed as "''S'' is necessary and sufficient for ''N'' ", "''S'' if and only if ''N'' ", or .

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Necessity and sufficiency」の詳細全文を読む



スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース

Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.