Let $G$ be an undirected connected graph with distinct edge weight. Let $E_{\text{max}}$ be the edge with maximum weight and $E_{\text{min}}$ the edge with minimum weight. Which of the following statements is false?
- Every minimum spanning tree of $G$ must contain $E_{\text{min}}$
- If $E_{\text{max}}$ is in minimum spanning tree, then its removal must disconnect $G$
- No minimum spanning tree contains $E_{\text{max}}$
- $G$ has a unique minimum spanning tree