This question asks you to define a SCHEME function that computes the Bell numbers. The nth Bell number is the number of partitions" of n objects. To be precise, it is the number of ways to write the set {1,...,n} as a union of a family of disjoint subsets. Equivalently, it is the number of ways to take n items and arrange them into piles. For example, B3, the 3th Bell number, is equal to 5 because the set {1,2,3} has 5 different partitions: {1,2,3}, {1,2} U {3}, {1,3} {2} {1}U {2,3}, and {1} U {2} {3}. It might be worth defining the function b(n, k) equal to the number of ways that {1,...,n} can be expressed as a partition into exactly k sets; note then that Bn = bin, 1) + ... + b(n, n). Note, also, that the bin, k) satisfy a rather nice recursive relationship: bín, k) = k. b(n - 1,k) + b(n - 1, k-1). (To see this, notice that partitions of {1,...,n} can be divided into two different types: those where n is by itself in a singleton set), and those where it appears with some other elements. If you remove the element n from the first type of partition, you obtain a partition of n-1 objects into k-1 sets—there are bin - 1, k-1) of these; if you remove n from the second type of partition, you obtain a partition of n-1 objects into k sets—there are b(n-1,k) of these.) Use this recursive rule to give a simple SCHEME definition for B. If you define a separate auxiliary function to compute b(n, k), make sure you keep it local to your function that computes the Bell number.