# Sole sufficient operator

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
A sole sufficient operator or a sole sufficient connective is an operator that is sufficient by itself to generate all of the operators in a specified class of operators. In logic, it is a logical operator that suffices to generate all of the boolean-valued functions, $$f : X \to \mathbb{B}$$, where $$X\!$$ is an arbitrary set and where $$\mathbb{B}$$ is a generic 2-element set, typically $$\mathbb{B} = \{ 0, 1 \} = \{ false, true \}$$, in particular, to generate all of the finitary boolean functions, $$f : \mathbb{B}^k \to \mathbb{B}$$.