NAND does not possess any of the following five properties, each of which is required to be absent from, and the absence of all of which is sufficient for, at least one member of a set of functionally complete operators: truth-preservation, falsity-preservation, linearity, monotonicity, self-duality.
This can also be realized as follows: All three elements of the functionally complete set {AND, OR, NOT} can be constructed using only NAND.