Given: An edge-weighted, undirected graph T. Find a subgraph T G such that T connects all vertices of G The weight of T is minimized Acyclic Connected Undirected. (Hence a tree.) Number of edges: |V| - 1 May not be unique. Build a set A of edges Start with A = 0 Add edges while maintaining loop invariant: Invariant: A is a subset of some MST Call an edge (u, v) safe for A iff A U {(u, v)} is also a subset of some MST. So we only add safe edges. For MST problems, we are always dealing with undirected, weighted graphs. The algorithms used below can be found in the slides. Find an example of a connected graph G = (V, E), a subset A E that is included in a minimum spanning tree, a cut (S, V\S), and an edge (u, v), such that (u, v) is a safe edge but not a light edge. Justify your assertions