Boolean Algebra, Logic and Quantifiers

Abstract

Boolean algebra was introduced in$$1854$$ by George Boole and has been very important for the development of computer science. It operates with variables which have the truth values true and false (sometimes denoted 1 and 0 respectively). In this chapter the main operations of Boolean algebra (conjunction (AND,$$\wedge $$ ), disjunction (OR,$$\vee $$ ) and negation (NOT,$$\lnot $$ )) are defined, and statements involving logical variables are studied with the aid of truth tables and Venn diagrams. Useful formulae involving logical variables are then discussed (De Morgan’s laws), along with the existential and universal quantifiers and their negation.