And similarly, if less than half the strings are generated, there must be some string for which neither that string nor its negation ever appear, implying that the system is incomplete.

So for ordinary logic both Nand and Nor work.

For n = 2 , the largest number of such operations is 6, achieved by Nor ; for n = 3 , it is 14, achieved by Xor (rule 150); for n = 4 , it is 27, achieved by rule 5737, which is Not[Xor[##]] & except when all inputs are True .

And this means that neither the Riemann tensor, nor a so-called Schild ladder for parallel transport, can readily be constructed.