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Directory:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 16:08, 12 May 2008
, 16:08, 12 May 2008→Casual introduction: add simpler example
==Casual introduction==
==Casual introduction==
Consider the situation represented by the following venn diagram.
<center><pre>
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| X . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
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| . . . . . . o-------------o . . . . . . . . . . . . . . . |
| . . h . . ./. . . . . . . .\. . . . . . . . . . . . . . . |
| . . @ . . / . . . . . . . . \ . . . . . . . . . . . . . . |
| . . . . ./. . i . . . . . . .\. . . . . . . . . . . . . . |
| . . . . / . . @ . . . . . . . \ . . . . . . . . . . . . . |
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| . . . o . . . . . . . . . . j . o . . . . . . . . . . . . |
| . . . | . . . . . . . . . . @ . | . . . . . . . . . . . . |
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| . . . | . . . . . .Q. . . . . . | . . . . . . . . . . . . |
| . . . | . . . . . . . . . . . . | . . . . . k . . . . . . |
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| . . . o . . . . . . . . . . . . o . . . . . . . . . . . . |
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| . . . . . .\. . . . . . . ./. . . . . . . . . . . . . . . |
| . . . . . . o-------------o . . . . . . . . . . . . . . . |
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</pre>
'''Figure 1. Local Habitations and Names'''
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The area of the rectangle represents a universe of discourse, <math>X.\!</math> This might be a population of individuals having various additional properties or it might be a collection of locations that various individuals occupy. The area of the "circle" represents the individuals that have the property <math>q\!</math> or the locations that fall within the corresponding region <math>Q.\!</math> Four individuals, <math>h, i, j, k,\!</math> are singled out by name. It happens that <math>i\!</math> and <math>j\!</math> currently reside in region <math>Q\!</math> while <math>h\!</math> and <math>k\!</math> do not.
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