In case you had no idea how to start to solve some of the homework problems, here is a little guide made by Oliver
DISCLAIMER: this is not a model submission that would have gotten full score. Oliver was sloppy with reference for time sake (he has stopped worked on Friday). In other points he has just referenced to other part of the homework without explaining how to modify the proof (this would have resulted in a 0 in the homework). Sometimes he has also explained way too many details :)
In any case, I hope this helps you.
I will not answer any mail in which you compare your solution to this asking for extra points, as said this is just a guide in case you did not know where to put your hands
Best
Sofia