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