Sole sufficient operator

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

Resources

• Logic Syllabus

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, Wikiversity
• Sole Sufficient Operator, Wikipedia