# Sole sufficient operator

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A sole sufficient operator is an operator that is sufficient by itself to generate every operator in a specified class of operators.  In the context of logic, it is a logical operator that suffices to generate every boolean-valued function, $$f : X \to \mathbb{B},\!$$ where $$X\!$$ is an arbitrary set and where $$\mathbb{B}\!$$ is a generic two-element set, typically $$\mathbb{B} = \{ 0, 1 \} = \{ \mathrm{false}, \mathrm{true} \},\!$$ in particular, to generate every finitary boolean function, $$f : \mathbb{B}^k \to \mathbb{B}.\!$$

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## Document history

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.