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Sole sufficient operator

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This page belongs to resource collections on Logic and Inquiry.

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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