Symbols:Greek/Nu/Minimal Negation Operator

Minimal Negation Operator

$\nu_k$

Let $\Bbb B$ be a Boolean domain:

$\Bbb B = \set {\F, \T}$

The minimal negation operator $\nu$ is a multiary operator:

$\nu_k: \Bbb B^k \to \Bbb B$

where:

$k \in \N$ is a natural number

$\nu_k$ is a boolean function defined as:

$\map {\nu_k} {x_1, x_2, \ldots, x_k} = \begin {cases}

\T & : \exists! x_j \in \set {x_1, x_2, \ldots, x_k}: x_j = \F \\ \F & : \text {otherwise} \end{cases}$

That is:

$\map {\nu_k} {x_1, x_2, \ldots, x_k}$ is true if and only if exactly one of its arguments is false.

The $\LaTeX$ code for \(\nu_k\) is \nu_k .