• Chinese: 足够, 使满足, 满足需要
• Dutch: genoeg zijn, volstaan, voldoen
• French: suffire
• German: ausreichen
• Portuguese: ser suficiente, atender, satisfazer

• Dutch: voldoen (aan)

• ttbc French: suffire 2,3
• ttbc Icelandic: duga
• ttbc Spanish: alcanzar

This article discusses only the formal meanings of necessary and sufficient. For the causal meanings see causation.

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.

• A sufficient condition is one that, if satisfied, assures the statement's truth. Formally, a statement P is a sufficient condition of a statement Q if P implies Q. Thus, jumping is sufficient to leave the ground, since an intrinsic element of the concept jumping'' is leaving the ground. A number's being divisible by 2 is sufficient for its being even.

• That a condition is one of necessary and sufficient does not imply the other. For instance, being a mammal is necessary but not sufficient to being human, and that a number q is rational is sufficient but not necessary to q‘s being a real number. A condition can be both necessary and sufficient. For example, at present, "today is the Fourth of July" is a necessary and sufficient condition for "today is Independence Day in the United States." Similarly, a necessary and sufficient condition for invertibility of a matrix M is that M have a nonzero determinant.

Necessary conditions

• Material implication
• Wason selection task
• Closed concept

Argument forms involving necessary and sufficient conditions

• Modus ponens
• Modus tollens (both valid)
• Affirming the consequent
• Denying the antecedent (both fallacious)

External links

• Stanford Encyclopedia of Philosophy: Necessary and Sufficient Conditions
• Critical thinking web tutorial: Necessary and Sufficient Conditions
• Simon Fraser University: Concepts with examples

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