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The '''minimal negation operator''' <math>\nu\!</math> is a [[multigrade operator]] <math>(\nu_k)_{k \in \mathbb{N}}</math> where each <math>\nu_k\!</math> is a <math>k\!</math>-ary [[boolean function]] <math>\nu_k : \mathbb{B}^k \to \mathbb{B}</math> defined in such a way that <math>\nu_k (x_1, \ldots , x_k) = 1</math> in just those cases where exactly one of the arguments <math>x_j\!</math> is <math>0.\!</math>

The '''minimal negation operator''' <math>\nu\!</math> is a [[multigrade operator]] <math>(\nu_k)_{k \in \mathbb{N}}</math> where each <math>\nu_k\!</math> is a <math>k\!</math>-ary [[boolean function]] defined in such a way that <math>\nu_k (x_1, \ldots , x_k) = 1</math> in just those cases where exactly one of the arguments <math>x_j\!</math> is <math>0.\!</math>

In contexts where the initial letter <math>\nu\!</math> is understood, the minimal negation operators can be indicated by argument lists in parentheses.  In the following text a distinctive typeface will be used for logical expressions based on minimal negation operators, for example, <math>\texttt{(x, y, z)}</math> = <math>\nu (x, y, z).\!</math>

In contexts where the initial letter <math>\nu\!</math> is understood, the minimal negation operators can be indicated by argument lists in parentheses.  In the following text a distinctive typeface will be used for logical expressions based on minimal negation operators, for example, <math>\texttt{(x, y, z)}</math> = <math>\nu (x, y, z).\!</math>

For example, consider two cases at opposite vertices of the cube:

For example, consider two cases at opposite vertices of the cube:

{| align="center" cellpadding="8" width="90%"

{| align="center" cellpadding="4" width="90%"

| valign="top" | <big>&bull;</big>

| valign="top" | <big>&bull;</big>

| The point <math>(1, 1, \ldots , 1, 1)</math> with all 1's as coordinates is the point where the conjunction of all posited variables evaluates to <math>1,\!</math> namely, the point where:

| The point <math>(1, 1, \ldots , 1, 1)</math> with all 1's as coordinates is the point where the conjunction of all posited variables evaluates to <math>1,\!</math> namely, the point where: