Recall the definition of the cut property in the context of Minimum Spanning Trees (MSTs) and how it relates to Kruskal's algorithm.

Analyze how Kruskal's algorithm selects edges in increasing order of weight and how this choice interacts with the cut property to ensure correctness.

Prove that Kruskal's algorithm maintains the cut property at every step by induction, showing that adding the next smallest edge does not violate the MST property.