Given an undirected weighted graph $G = (V, E)$ with non-negative edge weights, we can compute a minimum cost spanning tree $T = (V, E')$. We can also compute, for a given source vertex $s \epsilon V$ , the shortest paths from s to every other vertex in $V$. We now increase the weight of every edge in the graph by 1. Are the following true or false, regardless of the structure of $G$? Give a mathematically sound argument if you claim the statement is true or a counterexample if the statement is false.
$T$ is still a minimum cost spanning tree of $G$.