Boolean Algebra

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Boolean algebra, as developed in 1854 by George Boole in his book An Investigation of the Laws of Thought, is a variant of ordinary elementary algebra differing in its values, operations, and laws. Instead of the usual algebra of numbers, Boolean algebra is the algebra of truth values 0 and 1, or equivalently of subsets of a given set. The operations are usually taken to be conjunction ¿, disjunction ¿, and negation ¬, with constants 0 and 1. And the laws are definable as those equations that hold for all values of their variables, for example x¿(y¿x) = x. Applications include mathematical logic, digital logic, computer programming, set theory, and statistics. Boole's algebra predated the modern developments in abstract algebra and mathematical logic; it is however seen as connected to the origins of both fields.