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High Quality Content by WIKIPEDIA articles! In logic, the words necessity and sufficiency refer to the 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. A necessary condition of a statement must be satisfied for the statement to be true. Formally, a statement P is a necessary condition of a statement Q if Q implies P. For example, the ability to breathe is necessary to a human's survival. Likewise, for the whole numbers greater than two, being odd is necessary to being prime, since two is the only whole number that is both even and prime.