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 algorithms 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. Do not forget to give an efficient algorithm, proof of correctness and runtime analysis.

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.