Disjunktiivset

Disjunktiivset is the Estonian term for disjunctive, used to describe constructions that express alternatives or a choice between options. In logic and mathematics, it denotes a relation or operation that combines options into a group from which one or more may be chosen. In this article we discuss its general sense and applications across disciplines.

In logic, the disjunction of two statements A and B, written as A ∨ B, is true if either A is true, or B is true, or both. The disjunction is commutative and associative and distributes over conjunction. A distinction is made between inclusive disjunction (A ∨ B), which allows both operands to be true, and exclusive disjunction (A ⊕ B), which is true only when exactly one operand is true. In propositional logic, many expressions can be transformed into disjunctive normal form (DNF), a disjunction of conjunctions of literals.

In set theory and probability, disjunction corresponds to the union operation: an element belongs to A ∪ B if it belongs to A or to B (or both). In computer science, the disjunction operator OR is used in boolean expressions and control flow, often with short-circuit evaluation.

In linguistics and grammar, the disjunctive relates to expressions of alternatives, typically realized by conjunctions such as or, or phrases like either… or. The term disjunct refers to a single alternative within a disjunction.

Etymology: from Latin disjunctus, meaning separated or joined apart, reflecting the sense of linking alternatives while distinguishing them as choices. See also disjunction, exclusive or, disjunctive normal form, and union.