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.