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Encyclopedia > Sole sufficient operator

Sole sufficient operator, or sole sufficient connective, is a term used to describe an operator that is sufficient by itself to generate all of the operators in a specified class of operators. As used in logic, the term refers to 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} = left { 0, 1 right } = left { false, true right }, in particular, to generate all of the finitary boolean functions, f : mathbb{B}^k to mathbb{B}. Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...


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