Boolean algebra is a branch of algebra concerned with variables whose values are truth values, true and false, usually denoted with the integers 0 and 1 respectively. The set of these truth values is known as a boolean domain. The Boolean domain acts the same way as the twoelement set Integer Modulo 2. Boolean algebra is named after George Boole.
The basic operations of Boolean algebra are Conjunction (), Disjunction (), and Negation (). The operations can be defined as:
where .
They can also be defined using a table called a truth table:




OperationsEdit
The operations on the boolean domain are known as booleanvalued operations. These include conjunction, disjunction, and negation. Here are more:
 Material conditional: ()
 Exclusive disjuction: ()
 Bicondional: ()
Boolean lawsEdit
Law Name:  Law: 

Associativity of disjunction  
Associativity of conjunction 

Commutativity of disjunction  
Commutativity of conjunction  
Distributivity of conjunction over disjunction  
Identity for disjunction  
Identity for conjunction  
Annihilator for disjunction  
Annihilator for conjunction  
Idempotence of disjunction  
Idempotence of conjunction  
Absorption 1  
Absorption 2  
Complementation 1:  
Complementation 2:  
Double negation  
DeMorgan's laws 

Distributivity of disjunction over conjunction 
ApplicationsEdit
LogicEdit
Boolean algebra is often used to define the semantics of several formal systems, such as classical propositional logic . Many concepts of syntax in those formal systems come from Boolean logic. These logic systems are referred to as Boolean logic.
ComputingEdit
Boolean logic is often used for logic gates in computers.