my teacher wants us to think a conjecture for the invertible relation and then prove it, but I have absolutely no idea how to find that conjecture. Any help is appreciated.
, we define
like a relation is invertible with respect to if and only if (what condition does R has to satisfy?)
Also, by being invertible you mean that there exists an such that or ( ) where is the diagonal relation?
Probably this has something to do with surjection and injection. It is well-known that a function is an injection iff it has a left inverse, and is a surjection iff it has a right inverse (I hope I did not mix it up). Maybe something similar is expected here.