Sole sufficient operator

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

Focal nodes

 * Inquiry Live
 * Logic Live

Peer nodes

 * Sole Sufficient Operator @ InterSciWiki
 * Sole Sufficient Operator @ MyWikiBiz
 * Sole Sufficient Operator @ Subject Wikis
 * Sole Sufficient Operator @ Wikiversity
 * Sole Sufficient Operator @ Wikiversity Beta

Logical operators

 * Exclusive disjunction
 * Logical conjunction
 * Logical disjunction
 * Logical equality


 * Logical implication
 * Logical NAND
 * Logical NNOR
 * Negation

Related topics

 * Ampheck
 * Boolean domain
 * Boolean function
 * Boolean-valued function
 * Differential logic


 * Logical graph
 * Minimal negation operator
 * Multigrade operator
 * Parametric operator
 * Peirce's law


 * Propositional calculus
 * Sole sufficient operator
 * Truth table
 * Universe of discourse
 * Zeroth order logic

Relational concepts

 * Continuous predicate
 * Hypostatic abstraction
 * Logic of relatives
 * Logical matrix


 * Relation
 * Relation composition
 * Relation construction
 * Relation reduction


 * Relation theory
 * Relative term
 * Sign relation
 * Triadic relation

Information, Inquiry

 * Inquiry
 * Dynamics of inquiry


 * Semeiotic
 * Logic of information


 * Descriptive science
 * Normative science


 * Pragmatic maxim
 * Truth theory

Related articles

 * Cactus Language
 * Futures Of Logical Graphs
 * Propositional Equation Reasoning Systems


 * Differential Logic : Introduction
 * Differential Propositional Calculus
 * Differential Logic and Dynamic Systems


 * Prospects for Inquiry Driven Systems
 * Introduction to Inquiry Driven Systems
 * Inquiry Driven Systems : Inquiry Into Inquiry

Document history
Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.


 * Sole Sufficient Operator, InterSciWiki
 * Sole Sufficient Operator, MyWikiBiz
 * Sole Sufficient Operator, PlanetMath
 * Sole Sufficient Operator, SemanticWeb
 * Sole Sufficient Operator, Wikinfo
 * Sole Sufficient Operator, Wikiversity
 * Sole Sufficient Operator, Wikiversity Beta
 * Sole Sufficient Operator, Wikipedia