Boolean Algebra

In 1849, George Boole published a scheme for the algebraic description of processes involved in logical thought and reasoning, known as Boolean algebra.

Boolean Algebra poses a set of rules used to simplify the given logic expression without changing its functionality.

Axioms of Boolean Algebra

Single-Variable Theorems If is a variable in , then the following theorems hold:

Principle of Duality

Given a logic expression, its dual is obtained by replacing all + operators with · operators, and vice versa, and by replacing all 0s with 1s, and vice versa.

The dual of any true statement (axiom or theorem) in Boolean algebra is also a true statement. This is based on De Morgan’s Laws (DML).

title: Why duality?
Duality implies that at least two different ways exist to express every logic function with Boolean algebra. Often, one expression leads to a simpler physical implementation than the other and is thus preferable.

Duality of Canonical Forms

Two- and Three-Variable Properties

If x, y, and z are the variables in , then the following properties hold:

This review on boolean algebra is super helpful.