Can you throw us some hint? :)
I think it's easier to see how to solve this when you consider how Kruskal finds the MSTs.
Also, first look for an algorithm that checks if there is a single MST in the graph.
But, it will work with Prim also right? (as told in the "Tirgul") :)
Perhaps I am missing something, but it seems to me that it will be drastically harder to use Prim in this case.
What was told in the tirgul about this?