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 p | q | p nand q
---+---+----------
...
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)

 p | q | p nor q
---+---+---------
...
p and q === (p nor p) nor (q nor q)
p or q  === (p nor q) nor (p nor q)
p xor q === [something very long]