Union
$$A \cup B =$$
{ achiever, beauty, crown, explorer, foundation, glory, killer, kingdom, mercy, severity, socializer, understanding, victory, wisdom }
Symmetric Difference
$$A \ominus B =$$
{ achiever, beauty, crown, explorer, foundation, glory, killer, kingdom, mercy, severity, socializer, understanding, victory, wisdom }
Cartesian Product
$$A \times B =$$
{ (achiever, beauty),
(achiever, crown),
(achiever, foundation),
(achiever, glory),
(achiever, kingdom),
(achiever, mercy),
(achiever, severity),
(achiever, understanding),
(achiever, victory),
(achiever, wisdom),
(explorer, beauty),
(explorer, crown),
(explorer, foundation),
(explorer, glory),
(explorer, kingdom),
(explorer, mercy),
(explorer, severity),
(explorer, understanding),
(explorer, victory),
(explorer, wisdom),
(killer, beauty),
(killer, crown),
(killer, foundation),
(killer, glory),
(killer, kingdom),
(killer, mercy),
(killer, severity),
(killer, understanding),
(killer, victory),
(killer, wisdom),
(socializer, beauty),
(socializer, crown),
(socializer, foundation),
(socializer, glory),
(socializer, kingdom),
(socializer, mercy),
(socializer, severity),
(socializer, understanding),
(socializer, victory),
(socializer, wisdom) }
Bartle taxonomy of player types