Exercise 2.32.  We can represent a set as a list of distinct elements, 
and we can represent the set of all subsets of the set as a list of 
lists. For example, if the set is (1 2 3), then the set of all subsets 
is (() (3) (2) (2 3) (1) (1 3) (1 2) (1 2 3)). Complete the following 
definition of a procedure that generates the set of subsets of a set and 
give a clear explanation of why it works:

(define (subsets s)
  (if (null? s)
      (list nil)
      (let ((rest (subsets (cdr s))))
        (append rest (map <??> rest)))))

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(define (subsets s)
  (if (null? s)
      (list nil)
      (let ((rest (subsets (cdr s))))
        (append rest (map (lambda (l) (cons (car s) l)) rest)))))

If the list is empty, the set of subsets is (()).

Otherwise, take as given the result R that would be obtained if the 
first member of the set were absent (i.e. the subsets of the cdr of 
the list).

Clearly, every member of R is a subset of the set, by transitivity, 
and no member of R contains the first member of the set, since elements 
of the set are distinct.

Our result then must include R which is the subsets that do not contain 
the first element, as well as every additional subset that does.