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sole sufficient operator (Definition)

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



"sole sufficient operator" is owned by Jon Awbrey.
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Other names:  sole sufficient connective

Cross-references: boolean functions, boolean-valued functions, operators, operator

This is version 1 of sole sufficient operator, born on 2010-05-11.
Object id is 866, canonical name is SoleSufficientOperator.
Accessed 700 times total.

Classification:
Physics Classification: 02. (Mathematical methods in physics)
 02.10.Ab (Logic and set theory)
 02.10.Hh (Rings and algebras)
 02.10.Ox (Combinatorics; graph theory)
 02.50.Cw (Probability theory)
 02.50.Tt (Inference methods)
 02.70.Wz (Symbolic computation )
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