Consider an undirected graph, G $=($V$,$ E$)$ with non$-$negative edge weights such that w$($e$)>=1$e in E$.$ Suppose that you have computed a minimum spanning tree for G$,$ as well as the shortest paths to all nodes from a particular node s in V$.$ Decrease the weights of all edges in the graph, such that w$($e$)=$w$($e$)1$e in E$.$

a$.$ Does the MST of G change under this weight adjustment? Either provide an example of a graph for which it does change, or prove that it cannot change.

b$.$ Do the single$-$source shortest paths from s change? Either provide an example of a graph for which it does change, or prove that they cannot change.