Boolean Algebra

Boolean algebra is a branch of algebra in mathematics and mathematical logic. It differs from basic algebra in two ways. For starters, the variables’ values are the truth values true and false, which are usually denoted by 1 and 0, whereas in elementary algebra, the variables’ values are numbers. Second, Boolean algebra employs logical operators such as the conjunction (and) symbol, the disjunction (or) symbol, and the negation (not) symbol. In contrast, elementary algebra employs arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra, like elementary algebra, is a formal way of describing logical operations.

George Boole introduced Boolean algebra in his first book, The Mathematical Analysis of Logic(1847), and expanded on it in his An Investigation of the Laws of Thought (1854).  According to Huntington, Learning Management System, Sheffer proposed the term “Boolean algebra” in 1913, though Charles Sanders Peirce titled the first chapter of his “The Simplest Mathematics” “A Boolean Algebra with One Constant” in 1880.  Boolean algebra was critical in the development of digital electronics and is supported by all modern programming languages. This method is also used in statistics and set theory.