1 Five people, \(A , B , C , D\) and \(E\), are to be matched to five tasks, \(J , K , L , M\) and \(N\). The table shows the tasks that each person is able to undertake.
| Person | Task |
| \(A\) | \(J , N\) |
| \(B\) | \(J , L\) |
| \(C\) | \(L , N\) |
| \(D\) | \(M , N\) |
| \(E\) | \(K , M\) |
- Show this information on a bipartite graph.
- Initially, \(A\) is matched to task \(N , B\) to task \(J , C\) to task \(L\), and \(E\) to task \(M\).
Complete the alternating path \(D - M \ldots\), from this initial matching, to demonstrate how each person can be matched to a task.
(3 marks)