In the sentence 'She ate an apple', 'ate' is a transitive verb.
In mathematics, the transitive property states that if a = b and b = c, then a = c.
In graph theory, a transitive relation is one where if (a, b) and (b, c) are in the relation, then (a, c) is also in the relation.
Transitive inference is the ability to deduce a relationship between two items by knowing the relationships between each of the items and a third item.