necessary condition
McGraw-Hill Science & Technology Dictionary:
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necessary condition
(′nes·ə′ser·ē kən′dish·ən)
(mathematics) A mathematical statement that must be true if a given statement is true.
Dictionary of Cultural Literacy: Science:
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necessary condition
In mathematics, a condition that must be satisfied for a statement to be true, but that does not in and of itself make it true. For example, a necessary condition to become president of the United States is that a candidate be over thirty-five years of age, but just being over thirty-five does not make one president.
Oxford Dictionary of Mathematics:
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Necessary and Sufficient Condition
The implication q ⇒ p can be read as ‘if q, then p’. When this is true, it may be said that q is a sufficient condition for p; that is, the truth of the ‘condition’ q is sufficient to ensure the truth of p. This means that p is true if q is true. On the other hand, when the implication p ⇒ q holds, then q is a necessary condition for p; that is, the truth of the ‘condition’ q is a necessary consequence of the truth of p. This means that p is true only if q is true. When the implication between p and q holds both ways, p is true if and only if q is true, which may be written p ⇔ q . Then q is a necessary and sufficient condition for p.
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McGraw-Hill Science & Technology Dictionary
McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved.
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Dictionary of Cultural Literacy: Science
The New Dictionary of Cultural Literacy, Third Edition Edited by E.D. Hirsch, Jr., Joseph F. Kett, and James Trefil. Copyright © 2002 by Houghton Mifflin Company. Published by Houghton Mifflin. All rights reserved.
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