For each of the two questions below, decide whether the answer is (i) “Yes,” (ii) “No,” or (iii) "Unknown, because it would resolve the question of whether P = NP." Give a brief explanation of your answer.
(a) Let's define the decision version of the Interval Scheduling Problem from Chapter 4 as follows: Given a collection of intervals on a time-line, and a bound k, does the collection contain a subset of nonoverlapping intervals of size at least k?
Question: Is it the case that Interval Scheduling <P Vertex Cover?
(b) Question: Is it the case that Independent Set <P Interval Scheduling?
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