Given: the set of binary operators contain all unary and nullary operators as a subset.

There are 2^(2×2)=16 possible binary boolean operators. In order, they are: FALSE, *x* AND *y*, *x* AND NOT *y*, *x*, *y* AND NOT *x*, *y*, *x* XOR *y*, *x* OR *y*, *x* NOR *y*, *x* EQV *y*, NOT *y*, *x* OR NOT *y*, NOT *x*, *y* OR NOT *x*, *x* NAND *y*, and TRUE.