Boolean Algebra is a sub-discipline of algebra which deals with the truth values of specific variables. These truth variables can either be true or false, which are usually denoted in Boolean Algebra as 1 and 0 respectively. Instead of the traditional arithmetic operations seen in Elementary Algebra, Boolean Algebra is mainly concerned with three types of operations: conjunction (and), disjunction (or) and negation (not).
Conjunction is denoted as ∧
Disjunction is denoted as ∨
Negation is denoted as ¬
These operations do not behave like normal arithmetic operations. In Boolean Algebra 1+1 does not equal 2. Instead 1+1 may equal 0, with the + sign being the symbol for another Boolean Operation XOR. Thus, it can be seen that Boolean Algebra stands apart from the realm of Elementary Algebra – as it has its own set of rules and principles.
Boolean Algebra is prevalent in the study of electrical circuits, as a two valued Boolean algebra can be used to describe the operations of a two-valued electrical switching circuit. Thus, it can be seen that understanding Boolean Algebra is crucial for the modern study of Computer Science, Programming, Statistics and Digital Circuits.