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| ==Casual introduction== | | ==Casual introduction== |
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− | Consider the situation represented by the following venn diagram. | + | Consider the situation represented by the venn diagram in Figure 1. |
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| <center><pre> | | <center><pre> |
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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. | | 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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| + | Now consider the situation represented by the venn diagram in Figure 2. |
| + | |
| + | <center><pre> |
| + | o-----------------------------------------------------------o |
| + | | X . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
| + | | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
| + | | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
| + | | . . . . . . o-------------o . . . . . . . . . . . . . . . | |
| + | | . . h . . ./. . . . . . . .\. . . . . . . . . . . . . . . | |
| + | | . . @ . . / . . . . . . . . \ . . . . . . . . . . . . . . | |
| + | | . . . . ./. . i . . . . . . .\. . . . . . . . . . . . . . | |
| + | | . . . . / . . @ . . . . . . . \ . . . . . . . . . . . . . | |
| + | | . . . ./. . . . . . . . . . . .\. . . . . . . . . . . . . | |
| + | | . . . o . . . . . . . . . . . . o . . . . . j . . . . . . | |
| + | | . . . | . . . . . . . . . . . . | . . . . . @ . . . . . . | |
| + | | . . . | . . . . . . . . . . . . | . . . . . . . . . . . . | |
| + | | . . . | . . . . . .Q. . . . . . | . . . . . . . . . . . . | |
| + | | . . . | . . . . . . . . . . k . | . . . . . . . . . . . . | |
| + | | . . . | . . . . . . . . . . @ . | . . . . . . . . . . . . | |
| + | | . . . o . . . . . . . . . . . . o . . . . . . . . . . . . | |
| + | | . . . .\. . . . . . . . . . . ./. . . . . . . . . . . . . | |
| + | | . . . . \ . . . . . . . . . . / . . . . . . . . . . . . . | |
| + | | . . . . .\. . . . . . . . . ./. . . . . . . . . . . . . . | |
| + | | . . . . . \ . . . . . . . . / . . . . . . . . . . . . . . | |
| + | | . . . . . .\. . . . . . . ./. . . . . . . . . . . . . . . | |
| + | | . . . . . . o-------------o . . . . . . . . . . . . . . . | |
| + | | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
| + | | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
| + | | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |
| + | o-----------------------------------------------------------o |
| + | </pre> |
| + | '''Figure 2. Same Names, Different Habitations''' |
| + | </center> |
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| … | | … |