Три задачи на предикаты

(defun set-subsetp (set1 set2 &key (test #'eql))
  (every #'(lambda (item)
             (find item set2 :test test))
         set1))
 
(defun set-equalp (set1 set2 &key (test #'eql))
  (and (set-subsetp set1 set2 :test test)
       (set-subsetp set2 set1 :test test)))
 
(defun set-intersection (set1 set2 &key (test #'eql))
  (remove-duplicates
   (remove-if #'(lambda (item)
                  (not (and (find item set1 :test test)
                            (find item set2 :test test))))
              (append set1 set2)) :test test))

(defun equal-set (x y) (= (length x) (length y) (length (setof (append x y)))))
 
==> equal-set
 
(equal-set '(1 2 3) '(1 2 3))
 
==> T
 
(equal-set '(1 2 3) '(1 2 ))
 
==> NIL
 
(equal-set '(1 2 3) '(1 2 3 4))
 
==> NIL

(defun chk-subset (x y) (AND (< (length y) (length x)) 
                             (= (length x) (length (setof (append x y))))))
 
==> chk-subset
 
(chk-subset '(1 2 3) '(1 2))
 
==> T
 
(chk-subset '(1 2 3) '(1 4))
 
==> NIL

(defun cross (x y) 
  (let ((res nil))
       (dolist (i x res)
         (when (member i y) (setq res (cons i res))))))
 
==> cross
 
(cross '(1 2 3 4) '(3 4 5 6))
 
==> (4 3)