# sole sufficient operator

A sole sufficient operator or a sole sufficient connective is an operator that is sufficient by itself to define all of the operators in a specified set of operators.

In logical contexts this refers to a logical operator that suffices to define 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 $\mathbb{B}=\{0,1\}=\{\mathrm{false},\mathrm{true}\}$, in particular, to define all of the finitary Boolean functions, $f:\mathbb{B}^{k}\to\mathbb{B}$.

 Title sole sufficient operator Canonical name SoleSufficientOperator Date of creation 2013-03-22 17:51:52 Last modified on 2013-03-22 17:51:52 Owner Jon Awbrey (15246) Last modified by Jon Awbrey (15246) Numerical id 6 Author Jon Awbrey (15246) Entry type Definition Classification msc 03B70 Classification msc 03B35 Classification msc 03B22 Classification msc 03B05 Synonym sole sufficient connective Related topic Ampheck Related topic LogicalConnective