Boolean Functions

Definition: Boolean Function

A Boolean function is a function which takes and outputs tuples from whose elements come from a set of two elements.

NOTATION

Most commonly, the elements of such a set are denoted by $0$ and $1$. This means that Boolean functions are usually written in the following way:

$$f:\{0,1{\}}^m\to \{0,1{\}}^n$$

Sometimes, the labels $\mathrm{F}$ and $\mathrm{T}$ may be used instead of $0$ and $1$ because Boolean algebra is used ubiquitously in propositional logic.