Transitive

In the field of grammar, 'transitive' refers to a verb that requires one or more objects to convey a complete thought, indicating an action that is directed toward a recipient. In mathematics, particularly in relation to relations, 'transitive' describes a property whereby if a relation exists between the first and second elements, as well as between the second and third, it also exists between the first and third. This concept can also apply to logic and philosophy, emphasizing relationships and causal connections.

Transitive meaning with examples

• In the sentence 'She gave him a book,' the verb 'gave' is transitive as it requires both a subject and an object. Without the object 'a book,' the action would remain incomplete, demonstrating how transitive verbs function in language to convey clear meanings.
• Mathematically, if we have a relation R such that aRb and bRc implies aRc, then we can say that R is transitive. This means that the existence of connections between elements allows us to infer further connections, thus constructing a deeper understanding of set relationships and properties.
• In his research, Dr. Smith highlighted several transitive verbs that often confuse students, such as 'make' and 'call.' He provided exercises that required students to identify and correctly use transitive verbs within various contexts to solidify their understanding of this grammatical rule.
• In logic, the transitive property posits that if A = B and B = C, then it follows that A = C. This principle is essential in various logical proofs and mathematical demonstrations, showing how relationships between different entities can facilitate reasoning.