What is confluence? I got a worksheet at university last week, and the first task is: A relation $R$ of a set $M$ is confluent, if $ \forall x \in M \forall w_1,w_2 \in M :((xRw_1 \land xRw_2 ) \to \exists z \in M (w_1Rz \land w_2Rz)) $ . I don't get it. What is the relationship between $z$ and $w_1$, $w_2$ and $x$? They are all part of the same set but why implicate the first 2 relations $w_1Rz$ and $w_2Rz$ and how do I recognize if a set is confluent? Thanks for your help! PS: This is just the "introduction" to the task, which I want to do on my own.

Confluence is a property that a relation on a set may or may not have (as Willie Wong commented, what you wrote is a _definition_ , not a statement about some specific relation where you can check if the property holds or not).

Intuitively, as paw88789 comments, a relation is confluent if every time it branches off at some element $x$ to some elements $w_1$ and $w_2$, then it eventually closes back at a later element $z$. You might want to look up the relevant Wikipedia article for starters.