$G = (V,E)$ is an undirected simple graph in which each edge has a distinct weight, and $e$ is a particular edge of $G$. Which of the following statements about the minimum spanning trees (MSTs) of $G$ is/are TRUE? I. If $e$ is the lightest edge of some cycle in $G$, then every MST of $G$ includes $e$ II. If $e$ is the heaviest edge of some cycle in $G$, then every MST of $G$ excludes $e$

Let us analyze both statements for a connected undirected graph with distinct edge weights (which guarantees a unique MST):

1. Statement I is FALSE: The Cycle Property states that the strictly heaviest edge in any cycle cannot be in the MST. However, being the lightest edge of *some* cycle does not guarantee inclusion in the MST. For example, consider a 3-cycle where all three edges have large weights compared to other alternative paths in the graph. The lightest edge of this cycle might still be the heaviest edge in a cut, or it may not be part of the MST.

2. Statement II is TRUE: This is the standard Cycle Property of Minimum Spanning Trees: for any cycle $C$ in a graph $G$, the edge with the strictly largest weight in $C$ cannot be part of any MST. If an MST included this heaviest edge, removing it would disconnect the tree into two components, and there would be another edge in the cycle $C$ with a strictly smaller weight connecting the two components, yielding a spanning tree with a smaller total weight (a contradiction).

Therefore, only statement II is true, which corresponds to option (B).