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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
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