TRC: Select an ID if it appears on all measurements
I had to look up wikipedia because I did not know Tuple Relational Calculus. I did only  skim over that article. There are differnces in notation as far as I can  see.

But after activating my knowledge about formal logic I think you are right because

∀r ∈ Rainfall (...)


is true if Rainfall does not contain any tuples. In this case your query reduces to 

{ t | ∃s ∈ Station (t[station_id] = s[station_id]}


and this describes all tuples of Station

What I am missing in your notation is that is unclear which attributes the tuple t of the solution contains. So if you want to select station_id  then the query should start with something like

{ t: {station_id} | ...}


if one uses the notataion of the wiki article.

Maybe you can supply some reference to your notation.