Definition.Boolean function [boolean/def/boolean-function]

A Boolean function is a function

Though we tend to relax the codomain and simply consider functions from the Boolean cube

(and call the first type Boolean-valued functions).

We can make this work with any set of 2 things. Other natural choices are $\left\{0,1\right\}$, $\left\{\text{True},\text{False}\right\}$, or the two elements of the field ${𝔽}_2$ (which makes the domain ${𝔽}_2^{𝑛}$).