# Minimum cut with reversed edges

In a directed weighted graph with source $$s$$ and sink $$t$$, a minimum cut is a set of edges with minimum weight whose removal makes $$t$$ unreachable from $$s$$. Suppose we take a minimum cut (if there are several, choose one with the minimum number of edges). Is it true that if we reverse all edges in this minimum cut, then $$t$$ is unreachable from $$s$$?

The condition "choose one with the minimum number of edges" is necessary; otherwise suppose there is a single edge with weight $$0$$ from $$t$$ to $$s$$. Then this edge forms a minimum cut, but reversing it would make $$t$$ reachable from $$s$$.