transitive

Transitive is an adjective used in mathematics, logic, and linguistics to describe a property of a relation or a class of verbs that connects elements in a way that extends beyond a single step.

In mathematics and logic: A relation R on a set is transitive if whenever aRb and bRc, then aRc. Common examples include the less-than relation (a < b and b < c imply a < c) and the subset relation ⊆ (A ⊆ B and B ⊆ C imply A ⊆ C). The concept is central to theories of order and graphs; the transitive closure of a relation is the smallest transitive relation containing it, capturing all indirect connections.

In linguistics: A transitive verb takes a direct object, forming a subject–verb–object structure, as in "She read the book." In contrast, intransitive verbs do not require a direct object, as in "She slept." Some verbs can be both transitive and intransitive depending on usage; these ambitransitive verbs may either take an object or omit one. A ditransitive verb takes two objects, such as a direct object and an indirect object in sentences like "She gave him a gift." Transitivity also interacts with voice and syntax in various languages, with some marking object case or using different word orders to signal objecthood.