Necessary and sufficient conditions
|Part of the series on|
Necessary and sufficient conditions is a logical phrase that describes the relationship between two statements when one statement is true if and only if another statement is true. If a given statement is a necessary condition of another it must be true for the second statement to be true. If a given statement is a sufficient condition for another statement to be true the first statement, if satisfied as true, assures the second statement is true.
In physical science terms, a necessary and sufficient condition is known as the "cause" of an event, and the ensuing event is the "effect" of the prior one. The cause, of course, precedes the effect in time, although under the "necessary and sufficient" constraint, either event's occurrence can be imputed from the occurrence of the other.
In mathematics, "necessary and sufficient" is used to establish an equivalence relation between two statements: if the truth of one statement is necessary and sufficient for the truth of another statement, then the two statements are equivalent.