Changes

To pass from these limiting examples to the general case, observe that a singular proposition <math>s : \mathbb{B}^k \to \mathbb{B}</math> can be given canonical expression as a conjunction of literals, <math>s = e_1 e_2 \ldots e_{k-1} e_k</math>.  Then the proposition <math>\nu (e_1, e_2, \ldots, e_{k-1}, e_k)</math> is <math>1\!</math> on the points adjacent to the point where <math>s\!</math> is <math>1,\!</math> and 0 everywhere else on the cube.

To pass from these limiting examples to the general case, observe that a singular proposition <math>s : \mathbb{B}^k \to \mathbb{B}</math> can be given canonical expression as a conjunction of literals, <math>s = e_1 e_2 \ldots e_{k-1} e_k</math>.  Then the proposition <math>\nu (e_1, e_2, \ldots, e_{k-1}, e_k)</math> is <math>1\!</math> on the points adjacent to the point where <math>s\!</math> is <math>1,\!</math> and 0 everywhere else on the cube.

For example, consider the case where <math>k = 3.\!</math>  Then the minimal negation operation <math>\nu (p, q, r)\!</math>, when there is no risk of confusion written more simply as <math>(p, q, r)\!</math>, has the following venn diagram:

For example, consider the case where <math>k = 3.\!</math>  Then the minimal negation operation <math>\nu (p, q, r)\!</math> &mdash; written more simply as <math>\texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}</math> &mdash; has the following venn diagram:

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<p>[[Image:Minimal_Negation_Operator_1.jpg|500px]]</p>

<p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p>

<p><math>\text{Figure 2.} ~~ (p, q, r)</math>

<p><math>\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}</math>

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For a contrasting example, the boolean function expressed by the form <math>((p),(q),(r))\!</math> has the following venn diagram:

For a contrasting example, the boolean function expressed by the form <math>\texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math> has the following venn diagram:

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<p>[[Image:Minimal_Negation_Operator_2.jpg|500px]]</p>

<p>[[Image:Venn Diagram ((P),(Q),(R)).jpg|500px]]</p>

<p><math>\text{Figure 3.} ~~ ((p),(q),(r))</math>

<p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math>

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