$(15\%)$ For a given graph $G=(V,E),$ arbitrarily partition the nodes $V$ into two disjoint sets, $V_1$ and $V_2.$ Let $E_1$ be all the edges such that both nodes in the edge are in $V_1,E_2$ be all edges such that both nodes are in $V_2,$ and $E_3$ be all edges $(u,v)$ such that $uin{V}_1$ and $vin{V}_2.$ If we construct a minimum spanning tree $T_1$ on graph $(V_1,E_1)$ and a minimum spanning tree $T_2$ on $(V_2,E_2),$ then connect $T_1$ and $T_2$ on the lowestweighted edge connecting $T_1$ and $T_2.$ Will the connected result be a minimum spanning tree of $G?$ Proof the above method if it is correct, or give a counterexample.