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

In the conditional statement, "if S then N", the expression represented by S is called the antecedent and the expression represented by N is called the consequent. This conditional statement may be written in many equivalent ways, for instance, "N if S", "S implies N", "S only if N", "N is implied by S", S ⇒ N or "N whenever S".