# Sole sufficient operator

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Revision as of 21:26, 19 May 2007 by Jon Awbrey (talk | contribs) (copy text from [http://www.opencycle.net/ OpenCycle] of which Jon Awbrey is the sole author)

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