1 Five people, \(A , B , C , D\) and \(E\), are to be matched to five tasks, 1, 2, 3, 4 and 5. The table shows which tasks each person can do.
| Person | Tasks |
| \(A\) | \(1,3,5\) |
| \(B\) | 2,4 |
| \(C\) | 2 |
| \(D\) | 4,5 |
| \(E\) | 3,5 |
- Show this information on a bipartite graph.
- Initially \(A\) is matched to task 3, \(B\) to task 4, \(C\) to task 2 and \(E\) to task 5 .
Use an alternating path from this initial matching to find a complete matching.