Algorithms and Complexity problem

Minimum spanning tree Do problem 4.9 on page 192 of the textbook. For your convenience, here is the problem. Let G = (V, E) be a connected (undirected) graph with n vertices, m edges and positive edge costs (assume edge costs are distinct). Let T = (V, E') be a spanning tree of G. The bottleneck edge of T is the edge of T with the greatest cost. A spanning tree T of G is called a minimum bottleneck spanning tree where there exists no spanning tree of G with a cheaper bottleneck edge. Questions: (a) Is every minimum bottleneck tree of G a minimum spanning tree of G? Prove or give a counter-example, (b) Is every minimum spanning tree of G a minimum bottleneck tree of G? Prove or give a counter-example