Boolean Algebra

Abstract

Boolean is a set $\mathbb {B}=\{0,1\}$ with defined on it operations of disjunction ($\vee$), conjunction ($\wedge$), and negation ($\overline{\phantom {a}}$). Boolean variable p can take the values 0 or 1 (and only them), $p\in \mathbb {B}$. Boolean expression is formed by Boolean variables with the help of operations  $\vee$, $\wedge$, $\overline{\phantom {a}}$  and brackets. The function $f:\mathbb {B}^n\rightarrow \mathbb {B}$, where $f(x_1,\dots ,x_n)$ is Boolean expression, is called Boolean function. The most important classes of Boolean functions are considered:

• Functions that preserve constants 0 and 1.

• Self-dual functions.

• Linear functions.

• Monotone functions.