MyWikiBiz, Author Your Legacy — Sunday November 24, 2024
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, 03:30, 11 July 2008
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− | Propositional forms on two variables correspond to boolean functions ''f'' : '''B'''<sup>2</sup> → '''B'''. In Table 7 each function ''f''<sub>''i''</sub> is indexed by the values that it takes on the points of the universe ''X''<sup> •</sup> = [''x'', ''y''] <math>\cong</math> '''B'''<sup>2</sup>. Converting the binary index thus generated to a decimal equivalent, we obtain the functional nicknames that are listed in the first column. The 2<sup>2</sup> points of the universe ''X''<sup> •</sup> are coordinated as a space of type '''B'''<sup>2</sup>, as indicated under the heading of the Table, where the coordinate projections ''x'' and ''y'' run through the various combinations of their values in '''B'''. | + | Propositional forms on two variables correspond to boolean functions <math>f : \mathbb{B}^2 \to \mathbb{B}.</math> In Table 7 each function <math>f_i\!</math> is indexed by the values that it takes on the points of the universe <math>X^\circ = [x, y] \cong \mathbb{B}^2.</math> Converting the binary index thus generated to a decimal equivalent, we obtain the functional nicknames that are listed in the first column. The <math>2^2\!</math> points of the universe <math>X^\circ</math> are coordinated as a space of type <math>\mathbb{B}^2,</math> as indicated under the heading of the Table, where the coordinate projections <math>x\!</math> and <math>y\!</math> run through the various combinations of their values in <math>\mathbb{B}.</math> |
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