Assignment 3 - question 6b

I am a little confused by this question, and am hoping someone can help clear things up.

I have drawn the state space, no problems. My problem comes in where is says that a value of 1 is assigned to a leaf node if MIN wins, and 0 is otherwise. Maybe I am missing something, but shouldn't it be 0 if MIN wins?
MIN's objective is to go down the route of the minimum value - but if we assign a 0 to MIN not winning, surely MIN will always try to "not win", by trying to reach a leaf node of value 0?

Hope my explanation makes sense, and any insight would be appreciated.

I don't think it matters that much. It's just the goal state after all. I just followed the instructions exactly, and then did the min-max tree as normal. The end result is that a winning move exists, so I'm guessing it can't be far off.