Necessity and sufficiency

The sun being above the horizon is a necessary condition for direct sunlight; but it is not a sufficient condition as something else may be casting a shadow, e.g. in the case of an eclipse.

That a train runs on schedule can be a sufficient condition for arriving on time (if one boards the train and it departs on time, then one will arrive on time); but it is not always a necessary condition, since there are other ways to travel (if the train does not run to time, one could still arrive on time through other means of transport).

Consider two logical statements S and N, such that S is sufficient for N (if S is true, then N must also be true). Figuratively, if we are within S then we are within N. It follows that S cannot be true unless N is true – i.e., that N is a necessary condition for S.

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.

单词	Necessary cause
释义	Necessary cause 原声例句国富论（一） To complain of it, is to lament over the necessary cause and effect of the greatest public prosperity. 抱怨它，就是哀叹最大的公共繁荣的必要因果关系。英语百科 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.
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Necessary cause

Necessity and sufficiency