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Sole sufficient operator

MyWikiBiz, Author Your Legacy — Thursday August 07, 2008

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, $f : \mathbb{B}^k \to \mathbb{B}$ .