2 Five people \(A , B , C , D\) and \(E\) are to be matched to five tasks \(R , S , T , U\) and \(V\).
The table shows the tasks that each person is able to undertake.
| Person | Tasks |
| \(A\) | \(R , V\) |
| \(B\) | \(R , T\) |
| \(C\) | \(T , V\) |
| \(D\) | \(U , V\) |
| \(E\) | \(S , U\) |
- Show this information on a bipartite graph.
- Initially, \(A\) is matched to task \(V , B\) to task \(R , C\) to task \(T\), and \(E\) to task \(U\).
Demonstrate, by using an alternating path from this initial matching, how each person can be matched to a task.