In mathematics and in mathematical logic, Boolean algebra is the subarea of algebra dealing with two-valued logic with only sentential connectives. From the algebraic point of view these systems are complemented distributive lattices and therefore they are called Boolean lattices. These types of algebraic structures capture essential properties of both set operations and logical operations.

A Boolean algebra is a six-tuple consisting of a set A with two binary operations

(called disjunction/or) and

(conjunction/and), respectively equippped with

, such that the two binary operations satify distributive laws, and there is a unary operation called complement.

This last property means there is ¬a for every member a of set A and:

a∨¬a = 1 and a∧¬a = 0

where 1 is the identity element, 0 is the zero element, ¬a is the complement of a.

The two-element Boolean algebra is also used for circuit design.
In electrical engineering 0 and 1 represent the two different states of one bit in a digital circuit, typically high and low voltage, e.g.,

.
A kapcsolási algebra azt vizsgálja, hogy az ilyen kapcsolási elemekből összeállított háló kimenetén a lehetséges két állapot melyike valósul meg, ha az elemek az egyik vagy másik lehetséges állapotban vannak. Ezért a Boole-algebra az elektronikus digitális számítógép konstruálásának nélkülözhetetlen elméleti alapja.

We show Boolen Algebra with the above interpretation in this presentation.