# Sole sufficient operator

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, ${\displaystyle f:X\to \mathbb {B} ,\!}$ where ${\displaystyle X\!}$ is an arbitrary set and where ${\displaystyle \mathbb {B} \!}$ is a generic two-element set, typically ${\displaystyle \mathbb {B} =\{0,1\}=\{\mathrm {false} ,\mathrm {true} \},\!}$ in particular, to generate every finitary boolean function, ${\displaystyle f:\mathbb {B} ^{k}\to \mathbb {B} .\!}$

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