(define (is-empty-set? S) (if (eq? () S) #t #f) )

(define (member? S e)
  (cond
    ((is-empty-set? S) #f)
    ((eq? (car S) e) #t)
    (else (member? (cdr S) e))
  ))

(define (insert S e) (if (member? S e) S (cons e S)))

(define (delete S e)
  (cond
    ((is-empty-set? S) S)
    ((eq? (car S) e) (cdr S))
    (else (cons (car S) (delete (cdr S) e)) )
  ))

(define (union S A)
  (cond
    ((is-empty-set? S) A)
    ((is-empty-set? A) S)
    (else (append (union S (cdr A))
                  (if (member? S (car A)) () (list (car A)))
          ))))

(define (intersection A B)
  (cond
    ((is-empty-set? A) A)
    ((is-empty-set? B) B)
    (else (append (intersection B (cdr A))
                  (if (member? B (car A)) (list (car A)) ())
          ))))

(define (difference S A)
  (cond
    ((is-empty-set? S) S)
    ((is-empty-set? A) S)
    (else (append (difference (cdr S) A)
                  (if (member? A (car S)) () (list (car S)))
          ))))

(define (cardinality S) (length S))

(define (set-equal? A B)
  (if (and (eq? (cardinality A) (cardinality B))
           (eq? (difference A B) ()))
      #t
      #f
  ))

(define (power-set S)
  (cond
    ((is-empty-set? S) (list ()))
    (else (append (power-set (cdr S))
                  (map (lambda (a) (cons (car S) a)) (power-set (cdr S)))
;                  (list (list (car S)))
          ))))

(define (cartesian-product A B)
  (cond
    ((is-empty-set? A) A)
    ((is-empty-set? B) B)
    (else (append (cartesian-product (cdr A) B)
                  (map (lambda (b) (cons (car A) (list (list (car A) b)))) B)
          ))))