# 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 $x$ is a variable in $B$, then the following theorems hold:

### Principle of Duality

Given a logic expression, its dual is obtained by replacing all + operators with Â· 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 Morganâ€™s Laws (DML).

### Two- and Three-Variable Properties

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

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