I was reading the TECS book (The Elements of Computing Systems), in the book, we start to build the other logical gates with a single primitive logical gate, the $NAND$ gate. With it, we could easily make the $NOT$ gate, then the $AND$ gate and then the $OR$ gate.
With the $NOT$, $AND$ and $OR$ gates, we could express any truth table through cannonical representation.
The book has the table given below, I was wondering if we could do the same by taking any other boolean function as primitive, I'm quite sure that it's not possible to do with both constant $0$ nor constant $1$. What about the others?