Extra required problem:

i$)$ Show how a black$-$box solver for the Independent Set Problem could be used to solve the Interval Scheduling Problem that we saw when we studied Greedy algprithms early in the semester $($defined in chapter $1$ and revisited in chapter $3$ and on the midterm$).$ I.e$.,$ reduce the Interval Scheduling Problem to the Ind. 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.