In general, a combinatory logic basis needs a function of at least two variables. However, there are some unusual cases where a basis can be found with only one variable. For example, the basis {0, 1} is sufficient for propositional calculus. The reason you need at least two variables is that you need to be able to construct all possible truth tables from those two variables. With three variables, you can create 8 possible truth tables (2 raised to the 3rd power). That's enough to represent all logical functions that can be created from three variables.