Write the formal descriptions of the following sets: (a) the set containing the numbers 5, 9, and 27. (b) the set that contains all the natural numbers less than 2. (c) the set containing the empty string. (d) the set containing nothing at all.

Suppose you and your friend live on the same street d miles away from each other. between your house and your friend’s house there are n motorized scooters positioned at distances x1, x2, . . , xn miles from your house towards your friend’s house. each scooter has a battery that may or may not be fully charged. let’s say that the scooters can take you distances d1, d2, . . , dn miles down the road. each scooter also has a price p1, p2, . . , pn that it takes to activate. any time you encounter another scooter, you may take the new scooter and leave your old scooter behind. there is an additional scooter at your house that you start with and it can go distance d0 miles and it is free to activate: p0 = 0. you wish to go to your friend’s house minimizing the total amount of money spent activating the scooters. design a dynamic programming algorithm that returns the minimum cost to get to your friend’s house using scooters x0, . . , xn.