 where \((\cdotp)^{*}\) is the operation of taking the transitive closure. If R is a relation, then \((R)^{*}\) is R plus all the pairs missing to make R a transitive relation. Consider the three world model: With the relation \(\bigcup_{i\in\{a,b\}}R_{i}\), we can reach \(w_{3}\) from \(w_{1}\) in two steps, stopping over at \(w_{2}\). With \((\bigcup_{i\in\{a,b\}}R_{i})^{*}\), \(w_{3}\) is reachable in one step: By the newly added transitive link from \(w_{1}\) to \(w_{3}\).