Topic summary
Functionally complete
Extracted from the Wikipedia article Functional completeness.
Minimal functionally complete operator sets
When a single logical connective or Boolean operator is functionally complete by itself, it is called a Sheffer function or sometimes a sole sufficient operator. There are no unary operators with this property. NAND and NOR, which are dual to each other, are the only two binary Sheffer functions. These were discovered, but not published, by Charles Sanders Peirce around 1880, and rediscovered independently and published by Henry M. Sheffer in 1913. In digital electronics terminology, the binary NAND gate (↑) and the binary NOR gate (↓) are the only binary universal logic gates.