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For a third facet, identify every mathematical predicate N with the set T(N) of objects, events, or statements for which N holds true; then asserting the necessity of N for S is equivalent to claiming that T(N) is a superset of T(S), while asserting the sufficiency of S for N is equivalent to claiming that T(S) is a subset of T(N).
Peano axioms. Giuseppe Peano; Mathematical induction. Structural induction; Recursive definition; Naive set theory. Element (mathematics) Ur-element; Singleton (mathematics)
Pages in category "Necessity and sufficiency" The following 5 pages are in this category, out of 5 total. This list may not reflect recent changes. ...
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 ...
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
Modal fallacy – confusing necessity with sufficiency. A condition X is necessary for Y if X is required for even the possibility of Y. X does not bring about Y by itself, but if there is no X, there will be no Y. For example, oxygen is necessary for fire.
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