Gate2019 cs Q48

0. Let G be any connected, weighted, undirected graph.
I. G has a unique minimum spanning tree, if no two edges of G have the same weight.
II. G has a unique minimum spanning tree, if, for every cut of G, there is a unique minimum-weight edge crossing the cut.
Which of the above two statements is/are TRUE?

Answer
Comment
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Option : C
Explanation : If no two edges of G have same weight surely G will have unique spanning tree is true.
So I is true
Also if, for every cut of G, there is a unique minimum weight edge crossing the cut then G will have unique spanning tree is also true. So II is true
[Note: The converse of II is not true, but that is not relevant to this question]
So both I and II are true.
Option (C) is correct.

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