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True and false are the two fundamental truth values in classical binary logic, used to express the truth of propositions, statements, or predicates. In formal logic, a proposition is true if it corresponds to reality or a given model, and false otherwise. These values underpin boolean algebra and are central to how information is processed in computation and mathematics.

In computing and programming, boolean values are stored in a boolean data type. They may be represented directly as true and false, or mapped to numeric values such as 1 and 0. Many languages also support aliases (yes/no, on/off) or treat other values as truthy or falsy in conditional expressions.

History and theory: The modern treatment of truth values emerged from ancient logic and was formalized in the 19th and 20th centuries by George Boole and Gottlob Frege. Boole's algebra laid the groundwork for manipulating truth values with operators such as AND, OR, and NOT. The principle of bivalence, common in classical logic, holds that every proposition is either true or false. These foundations underlie digital logic, computer architectures, and many areas of mathematics.

Applications and variations: Truth tables show the outcomes of applying logical connectives to truth values. Boolean logic supports implication and equivalence as well as negation. In some systems, such as SQL, a third value unknown can arise, reflecting incomplete information. Some programming languages also include the concept of truthy and falsy values beyond strict true/false representations.