I´ve come across a problem regarding relation composition. The task is to show, whether a composition of two equivalence relations on a set X is again an equivalence on the set X.
I´ve tried some graphical solutions for some examples but I am not sure how to show this generally.
We know an equivalence must be symmetric, transitive and reflexive but how can I prove that it all applies in this situation? I believe I can manage to show this for a relation intersection but for the composition I donť know how.
I don´t really need a formal proof whether it is true or not, some graphical illustration of the general principle would suffice as I am just trying to understand this.