Can anyone explain to me how to
Prove that nand is functionally complete.
(To wit: if we let $p ∗ q$ mean $¬(p ∧ q)$, show that the other connectives, $∧$, $∨$, $¬$ and $→$ are expressible in terms of $∗$.)
I understand that logical function on a fixed set of inputs has a finite number of cases, but unsure how to put that into context.