Question: i$)$ Show how a black$-$box solver for the Independent Set Problem could be used to solve the Interval Scheduling Problem seen when studying Greedy algorithms $($defined in chapter $1$ and revisited in chapter $3$ of Jon kleinberg and Eva Tardos Algorithm Design Textbook$).$ I.e$.,$ reduce the Interval Scheduling Problem to the Independent Set Problem in poly$-$time. $($You can use the decision version of interval scheduling if you$$d like, defined in exercise $8\mathrm{.}1.)$

ii$)$ The fact that you$$ve reduced Interval Scheduling to Independent Set in part $($i$)$ indicates to us that one problem is $$at least as hard as$$ the other. State which is which, and explain why$/$how the reduction indicates this to you.