Walkthrough

Activities: [(1,4), (3,5), (0,6), (5,7), (8,9), (5,9)]. Sorted by end time: [(1,4), (3,5), (0,6), (5,7), (5,9), (8,9)]. $1.$ Select (1,4). Last end = $4$.

$2.$ (3,5): start $3$ < $4$. Conflicts. Skip.

$3.$ (0,6): start $0$ < $4$. Conflicts. Skip.

$4.$ (5,7): start $5$ >= $4$. Select! Last end = $7$.

$5.$ (5,9): start $5$ < $7$. Conflicts. Skip.

$6.$ (8,9): start $8$ >= $7$. Select! Last end = $9$. Selected: (1,4), (5,7), (8,9). Count: $3$. Notice each selection extends the timeline minimally.