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Similarly, a necessary and sufficient condition for invertibility of a matrix M is that M has a nonzero determinant. Mathematically speaking, necessity and sufficiency are dual to one another. For any statements S and N, the assertion that "N is necessary for S" is equivalent to the assertion that "S is sufficient for N". Another facet of this ...
Another form of logic puzzle, popular among puzzle enthusiasts and available in magazines dedicated to the subject, is a format in which the set-up to a scenario is given, as well as the object (for example, determine who brought what dog to a dog show, and what breed each dog was), certain clues are given ("neither Misty nor Rex is the German Shepherd"), and then the reader fills out a matrix ...
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods.
The most prominent modern interpretation of the collective action problem can be found in Mancur Olson's 1965 book The Logic of Collective Action. [6] In it, he addressed the accepted belief at the time by sociologists and political scientists that groups were necessary to further the interests of their members.
An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes.
A thought experiment by Aristotle to explore the concept of future contingents and the problem of determinism and free will. Aristotle's theses The formulas ¬ (¬ A → A) and ¬ (A → ¬A) in propositional logic; they are theorems in connexive logic but not in classical logic. [17] [18] [19] See also Boethius' theses. arity
The concept of productive matrix was developed by the economist Wassily Leontief (Nobel Prize in Economics in 1973) in order to model and analyze the relations between the different sectors of an economy. [1] The interdependency linkages between the latter can be examined by the input-output model with empirical data.
In vector logic, the matrix-vector structure of logical operators is an exact translation to the format of linear algebra of these Boolean polynomials, where the x and 1−x correspond to vectors s and n respectively (the same for y and 1−y). In the example of NAND, f(1,1)=n and f(1,0)=f(0,1)=f(0,0)=s and the matrix version becomes: