/* Original version of this file copyright 1999 by Michael Wester,
 * and retrieved from http://www.math.unm.edu/~wester/demos/SetTheory/problems.macsyma
 * circa 2006-10-23.
 *
 * Released under the terms of the GNU General Public License, version 2,
 * per message dated 2007-06-03 from Michael Wester to Robert Dodier
 * (contained in the file wester-gpl-permission-message.txt).
 *
 * See: "A Critique of the Mathematical Abilities of CA Systems"
 * by Michael Wester, pp 25--60 in
 * "Computer Algebra Systems: A Practical Guide", edited by Michael J. Wester
 * and published by John Wiley and Sons, Chichester, United Kingdom, 1999.
 */
/* ----------[ M a c s y m a ]---------- */
/* ---------- Initialization ---------- */
showtime: all$
prederror: false$
/* ---------- Set Theory ---------- */
x: '[a, b, b, c, c, c]$
y: '[d, c, b]$
z: '[b, e, b]$
/* [x \/ y \/ z, x /\ y /\ z] => [{a, b, c, d, e}, {b}] */
[union(x, y, z), intersect(x, y, z)];
/* x \/ y \/ z - x /\ y /\ z => {a, c, d, e} */
setdifference(%[1], %[2]);
remvalue(x, y, z)$
/* Cartesian product of sets => {(a, c), (a, d), (b, c), (b, d)} */
apply('append, outermap("[", [a, b], [c, d]));