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I think it should be false because there may be more than one edge with the same weight.

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    $\begingroup$ Welcome to Computer Science! What have you tried? Where did you get stuck? We do not want to just hand you the solution; we want you to gain understanding. However, as it is we do not know what your underlying problem is, so we can not begin to help. See here for tips on asking questions about exercise problems. If you are uncertain how to improve your question, why not ask around in Computer Science Chat? $\endgroup$ – Raphael Aug 15 '18 at 17:46
  • $\begingroup$ You are on the right track. Try to construct a concrete example in which the algorithm may have different outputs. $\endgroup$ – dave Aug 15 '18 at 21:22
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Your are right. A simplest example would be a triangle with weight 1, 1, 1.

Did you see the "Search on Computer Science" button on top of this page? You may search for "unique minimum spanning tree" for many pertinent questions and answers. Or just search for "minimum spanning tree" for many related questions and answers. In fact, that is also a popular tag in this site.

You may find two definitive questions and answers at Are all MST minimum spanning trees reachable by Kruskal and Prim? and When is the minimum spanning tree for a graph not unique.

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