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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