# Work τ

## Minimal Negation Operators

### JPG

The venn diagram for $\nu(p, q)$ is shown in Figure 2.

$\text{Figure 2.} ~~ \nu(p, q)$

The venn diagram for $\nu(p, q, r)$ is shown in Figure 3.

$\text{Figure 3.} ~~ \nu(p, q, r)$

### LaTeX

$\begin{matrix} \texttt{()} & = & \nu_0 & = & 0 & = & \mathrm{false} \\[6pt] \texttt{(} x \texttt{)} & = & \nu_1 (x) & = & \tilde{x} & = & x^\prime \\[6pt] \texttt{(} x \texttt{,} y \texttt{)} & = & \nu_2 (x, y) & = & \tilde{x}y \lor x\tilde{y} & = & x^\prime y \lor x y^\prime \\[6pt] \texttt{(} x \texttt{,} y \texttt{,} z \texttt{)} & = & \nu_3 (x, y, z) & = & \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z} & = & x^\prime y z \lor x y^\prime z \lor x y z^\prime \end{matrix}$