A Minimum-Bottleneck Spanning Tree (MBST) is a spanning tree of a connected undirected graph with positive edge weights chosen so its maximum edge weight is as small as possible. Given a spanning tree of an undirected graph G with distinct edge weights, we define its bottleneck edge as its edge with the largest weight; a spanning tree of G is a MBST if there is no spanning tree of G whose bottleneck edge has lower weight. (a) Is the MBST of a graph with distinct edge weights unique? Prove it if yes, or provide a counter-example if no. (b) Given a connected undirected graph G with distinct positive edge weights, is the minimum spanning tree of G also a minimum-bottleneck spanning tree of G? Prove it if yes, or provide a counter-example if no.