Time left $3$:$21$:$4$

Consider an arbitrary iteration of the generic MST algorithm that uses the Red and Blue Rules with the Red$-$Blue Invariant. The set B of blue edges at that point forms a forest of one or more blue components. By the Red$-$Blue Invariant we know that there is an MST T that contains B$.$ Assume we still have more than one blue component. Form a cut C by partitioning these blue components into two non$-$empty subsets. Consider an arbitrary edge e of $T$ that crosses the cut $C.$

a$.$ none of the other choices

b$.$ By the Red$-$Blue Invariant, edge e must be a minimum$-$weight cross edge of the cut $C.$

c$.$ By the Loop Invariant proof technique, we can trade off edge e with a smaller weight edge, hence improving the weight of $T.$

d$.$ Weight of edge e might be strictly larger than the minimum$-$weight cross edge of the cut C $.$