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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. (Equivalently, it is impossible to have P without Q , or the falsity of Q ensures the falsity of P .) [ 1 ] Similarly, P is sufficient for Q , because P being true always implies that Q is true, but P not being ...
A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]
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.
Contingency is one of three basic modes alongside necessity and possibility. In modal logic, a contingent statement stands in the modal realm between what is necessary and what is impossible, never crossing into the territory of either status. Contingent and necessary statements form the complete set of possible statements.
The Elephant Curve, also known as the Lakner-Milanovic graph or the global growth incidence curve, is a graph that illustrates the unequal distribution of income growth for individuals belonging to different income groups. [1] The original graph was published in 2013 and illustrates the change in income growth that occurred from 1988 to 2008 ...
In economics, income distribution covers how a country's total GDP is distributed amongst its population. [1] Economic theory and economic policy have long seen income and its distribution as a central concern. Unequal distribution of income causes economic inequality which is a concern in almost all countries around the world. [2] [3]
An example is shown in Fig. 6, where the purple line is the Pareto set corresponding to the indifference curves for the two consumers. The vocabulary used to describe different objects which are part of the Edgeworth box diverges.
Figure 1: An increase in the income, with the prices of all goods fixed, causes consumers to alter their choice of market basket. The extreme left and right indifference curves belong to different individuals with different preferences, while the three central indifference curves belong to one individual for whom the income-consumption curve is shown.