Changes

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<math>\begin{matrix}

<math>\begin{matrix}

(~)       & = & 0 & = & \operatorname{false}

\texttt{(~)}

& = & 0

& = & \operatorname{false}

\\[6pt]

\\[6pt]

(x)       & = & \tilde{x} & = & x'

\texttt{(} x \texttt{)}

& = &

\tilde{x}

& = & x^\prime

\\[6pt]

\\[6pt]

(x, y)   & = & \tilde{x}y \lor x\tilde{y} & = & x'y \lor xy'

\texttt{(} x, y \texttt{)}

& = &

\tilde{x}y \lor x\tilde{y}

& = &

x^\prime y \lor x y^\prime

\\[6pt]

\\[6pt]

(x, y, z) & = & \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z} & = & x'yz \lor xy'z \lor xyz'

\texttt{(} x, y, z \texttt{)}

& = &

\tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}

& = &

x^\prime y z \lor x y^\prime z \lor x y z^\prime

\end{matrix}</math>

\end{matrix}</math>

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It may also be noted that <math>(x, y)\!</math> is the same function as <math>x + y\!</math> and <math>x \ne y</math>, and that the inclusive disjunctions indicated for <math>(x, y)\!</math> and for <math>(x, y, z)\!</math> may be replaced with exclusive disjunctions without affecting the meaning, because the terms disjoined are already disjoint.  However, the function <math>(x, y, z)\!</math> is not the same thing as the function <math>x + y + z\!</math>.

It may also be noted that <math>\texttt{(} x, y \texttt{)}</math> is the same function as <math>x + y\!</math> and <math>x \ne y</math>, and that the inclusive disjunctions indicated for <math>\texttt{(} x, y \texttt{)}</math> and for <math>\texttt{(} x, y, z \texttt{)}</math> may be replaced with exclusive disjunctions without affecting the meaning, because the terms disjoined are already disjoint.  However, the function <math>\texttt{(} x, y, z \texttt{)}</math> is not the same thing as the function <math>x + y + z\!</math>.

The minimal negation operator ('''mno''') has a legion of aliases:  ''logical boundary operator'', ''[[limen|limen operator]]'', ''threshold operator'', or ''least action operator'', to name but a few.  The rationale for these names is visible in the [[venn diagram]]s of the corresponding operations on [[set]]s.

The minimal negation operator ('''mno''') has a legion of aliases:  ''logical boundary operator'', ''[[limen|limen operator]]'', ''threshold operator'', or ''least action operator'', to name but a few.  The rationale for these names is visible in the [[venn diagram]]s of the corresponding operations on [[set]]s.