or

Or is a coordinating conjunction used to indicate a choice between two or more elements, such as words, phrases, or clauses. It links alternatives and is common in questions, statements, and conditional sentences. In everyday language, or helps present options, express doubt, or denote possibilities, as in “tea or coffee” or “go now or wait.”

In formal logic and mathematics, or denotes disjunction. P or Q is true if P is true, or Q is true, or both. The inclusive OR is the standard interpretation in logic, and the symbol ∨ is used to denote disjunction. In set theory, the logical OR corresponds to the union of sets.

English usage often blends inclusive and exclusive sense. While or typically allows the possibility that both options occur, phrases like either X or Y may imply exclusivity. Context, emphasis, and wording such as “either … or” can steer interpretation toward one-or-the-other meaning.

In computing and programming, OR is a boolean operator. Most languages implement short-circuit evaluation, where the second operand is not evaluated if the first already determines the result. In some languages, or expressions return non-boolean values (for example, in Python, a or b returns the first truthy value). In digital circuits, OR gates implement logical disjunction.

Related concepts include exclusive OR (XOR), where exactly one input is true, and disjunction more broadly, which in logic corresponds to the union of conditions or possibilities.