Isn't it the other way around?
An n-ary operator can take any amount of arguments, so a binary operator is an n-ary operator and all binary operators are a subset of the n-ary operators. A binary operator always takes two arguments, so it can't be the superset of the n-ary operators, which can take any amount of arguments.
My goal however ist to make Wolfram:Alpha only use binary operators; with NAND/NOR as n-ary operators, it also supplies solutions where three or more arguments are fed into NAND/NOR, I'm trying to make it only use NANDs/NORs that take two arguments.