2. [10 marks] This problem is about a weighted version of theSet Cover problem. The input consists of: a set E of n elements,where each e ∈ E has a non-negative weight w(e); a collection S1, .. . , Sk where Si ⊆ E; and a number t. The problem is to pick t ofthe subsets Si to maximize the sum of the weights of the elementscovered. The goal of this question is to show that the obviousgreedy algorithm has approximation factor 1 − 1 e where e isEuler’s constant. The greedy algorithm first picks a set thatcovers the maximum
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