p | q | p nand q
---+---+----------
 0 | 0 |    1
 0 | 1 |    1
 1 | 0 |    1
 1 | 1 |    0

not p   === p nand p
p and q === (p nand q) nand (p nand q)
p or q  === (p nand p) nand (q nand q)
p xor q === (p nand (q nand q)) nand ((p nand p) nand q)