Like others, all you have to do is create separate functions for calculating the intersection, union and subtraction of two sets and call them from checkresult:
(define (checkresult a b)
(list (subtract a b)
(subtract b a)
(union a b)
(intersect a b)))
Here are some examples of union, intersection, and subtraction functions:
(define (element? x lst)
(cond ((null? lst)
((eq? x (car lst))
(
(define (union a b)
(cond ((null? b) a)
((element? (car b) a)
(union a (cdr b)))
(
(define (intersect a b)
(if (null? a) '()
(let ((included (element? (car a) b)))
(if (null? (cdr a))
(if included a '())
(if included
(cons (car a) (intersect (cdr a) b))
(intersect (cdr a) b))))))
(define (subtract a b)
(cond ((null? a) '())
((element? (car a) b)
(subtract (cdr a) b))
(#t (cons (car a) (subtract (cdr a) b)))))
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