The statement "An edge set S is called 'cut set' if removal of edges from S disconnects the graph" is wrong because it is not necessary for a cut set to contain all of the edges that disconnect the graph. A cut set can contain only a subset of the edges that disconnect the graph, as long as removing that subset of edges disconnects the graph.
For example, consider the following graph:
A -- B
| |
C -- D
This graph is connected, and the edge set {AB, CD} is a cut set. However, removing only one of these edges, say AB, does not disconnect the graph. The graph is still connected, with vertices A and C connected through vertex B. It is only when both AB and CD are removed that the graph is disconnected.
Therefore, a more accurate definition of a cut set is:
A cut set of a connected graph G is a subset of the edges of G such that removing all of the edges in the subset disconnects G.