$($Greedy Algorithm$)$ Not just any greedy approach to the activity$-$selection problem produces

a maximum$-$size set of mutually compatible activities.

$(1)$ Give an example to show that the approach of selecting the activity of least duration from

among those that are compatible with previously selected activities does not work.

$(2)$ Give an example to show that the approach of always selecting the compatible remaining

activity with the earliest start time does not work.