Boolean

Boolean refers to a system of logical values used to represent truth. In mathematics and computer science, a boolean value is either true or false. In programming, boolean is a data type that stores these values and is used to control flow and decision making.

The concept originates with George Boole, whose 19th-century work laid the foundations of Boolean algebra, a formal algebraic treatment of logical operators. Boolean algebra uses operators such as AND, OR, and NOT, with truth tables defining the result of each operation. De Morgan's laws describe how negation distributes over conjunction and disjunction, and the duality principle underpins many logical transformations.

Boolean algebra supports simplification and manipulation of logical expressions. Canonical forms, such as sum of products or product of sums, are used in optimizing digital logic and circuit design. Boolean logic underpins the design of digital circuits, switching theory, and error detection and correction methods.

In practical computing, boolean types are common in programming languages as a data type with values true and false, sometimes alongside null or undefined. Booleans are used in conditional statements, loops, and evaluations, and they underpin search predicates, decision-making in algorithms, and the control flow of software systems. The concept remains foundational to modern computing, digital electronics, and formal logic.