[Oops.] Question 7.2b page 268

[molloykp]

Consider the following undirected graph. For example:
A--B weight 1
B--C weight 1

Subsets are A,C and B. The graph has no cycles, so, it satisfies the second bullet in the question. There is a non-unique min weight edge that crosses the partition, yet, this has a unique spanning tree (since it is a tree on input). This appears to violate the "if and only if" condition set forth in the problem.

Am I misinterpreting the question?