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In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement : "If P then Q ", Q is necessary for P , because the truth of Q is guaranteed by the truth of P .
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In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
Among historians, his most widely studied work is his algebra book al-fakhri fi al-jabr wa al-muqabala, which survives from the medieval era in at least four copies. [ 6 ] He expounded the basic principles of hydrology [ 7 ] and this book reveals his profound knowledge of this science and has been described as the oldest extant text in this field.
Modal logic is a kind of logic used to represent statements about necessity and possibility.It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation.
In the previous version, the section on sufficient conditions had reversed which is the condition and which is the thing obtained. If you do it this way, it's hard to tell at a glance the main difference between necessary and sufficient: necessary is obtained-->condition, while sufficient is condition-->obtained.
Sufficiency finds a useful application in the Rao–Blackwell theorem, which states that if g(X) is any kind of estimator of θ, then typically the conditional expectation of g(X) given sufficient statistic T(X) is a better (in the sense of having lower variance) estimator of θ, and is never worse.
The origin of mathematics is of arguments and disagreements. Whether the birth of mathematics was by chance or induced by necessity during the development of similar subjects, such as physics, remains an area of contention. [29] [30] Many thinkers have contributed their ideas concerning the nature of mathematics.