Union
$$A \cup B =$$
{ achiever, arithmetic, astronomy, explorer, geometry, killer, music, socializer }
Symmetric Difference
$$A \ominus B =$$
{ achiever, arithmetic, astronomy, explorer, geometry, killer, music, socializer }
Difference
$$A - B =$$
{ achiever, explorer, killer, socializer }
Difference
$$B - A =$$
{ arithmetic, astronomy, geometry, music }
Cartesian Product
$$A \times B =$$
{ (achiever, arithmetic),
(achiever, astronomy),
(achiever, geometry),
(achiever, music),
(explorer, arithmetic),
(explorer, astronomy),
(explorer, geometry),
(explorer, music),
(killer, arithmetic),
(killer, astronomy),
(killer, geometry),
(killer, music),
(socializer, arithmetic),
(socializer, astronomy),
(socializer, geometry),
(socializer, music) }
Bartle taxonomy of player types