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In ordinary English (also natural language) "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. For example, being a man is a necessary condition for being a brother, but it is not sufficient—while being a man sibling is a necessary and sufficient condition for being a brother.
3. P is not necessary but it is sufficient: If (P OR Q) then S. We don't NEED P. We can get S from Q. But on the other hand if we DO have P, P is enough in itself to create S. No need for anything else. 4. P is not necessary AND not sufficient: If (P OR Q) AND R then S. P is not necessary. We can get S from Q even though we do not have P.
The absence these conditions guarantees the outcome cannot occur, and no other condition can overcome the lack of this condition. Further, necessary conditions are not always sufficient. For example, AIDS necessitates HIV, but HIV does not always cause AIDS. In such instances, the condition demonstrates its necessity but lacks sufficiency.
Necessary But Not Sufficient is a 2000 novel authored by Eliyahu Goldratt with co-authors Eli Schrangenheim and Carol A. Ptak. Necessary But Not Sufficient is written as a "business novel" and shows the fictional application of the theory of constraints to enterprise resource planning (ERP) and operations software and organizations using that software.
Example 1. One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example: If someone lives in San Diego, then they live in California. Joe lives in California. Therefore, Joe lives in San Diego. There are many places to live in California other than San Diego.
For a polynomial to be Hurwitz, it is necessary but not sufficient that all of its coefficients be positive (except for quadratic polynomials, which also imply sufficiency). A necessary and sufficient condition that a polynomial is Hurwitz is that it passes the Routh–Hurwitz stability criterion. A given polynomial can be efficiently tested to ...
Metaphysical necessity is contrasted with other types of necessity. For example, the philosophers of religion John Hick [2] and William L. Rowe [3] distinguished the following three: factual necessity (existential necessity): a factually necessary being is not causally dependent on any other being, while any other being is causally dependent on it.
For example, if a customer buys apples because he prefers them to blueberries, telling them that cherries are on sale should not make them buy blueberries instead of apples. John Harsanyi later strengthened this result by showing that if societies must make decisions under uncertainty , the unique social welfare function satisfying coherence ...