Finitary boolean function

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A finitary boolean function is a function of the type $f : \mathbb{B}^k \to \mathbb{B}$ , where $\mathbb{B}$ is a generic 2-element set, typically $\mathbb{B} = \left \{ 0, 1 \right \}$ , frequently interpreted for logical applications as $\mathbb{B} = \left \{ false, true \right \}$ , and where k is a positive integer.