Boolean Function

Boolean Function

In mathematics, a (finitary) Boolean function (or switching function) is a function of the form ƒ : Bk → B, where B = {0, 1} is a Boolean domain and k is a non-negative integer called the arity of the function. In the case where k = 0, the "function" is essentially a constant element of B.

Every k-ary Boolean formula can be expressed as a propositional formula in k variables x₁, …, x_k, and two propositional formulas are logically equivalent if and only if they express the same Boolean function. There are 22k k-ary functions for every k.