Union
$$A \cup B =$$
{ achiever, artha, dharma, explorer, kama, killer, moksha, socializer }
Symmetric Difference
$$A \ominus B =$$
{ achiever, artha, dharma, explorer, kama, killer, moksha, socializer }
Difference
$$A - B =$$
{ achiever, explorer, killer, socializer }
Difference
$$B - A =$$
{ artha, dharma, kama, moksha }
Cartesian Product
$$A \times B =$$
{ (achiever, artha),
(achiever, dharma),
(achiever, kama),
(achiever, moksha),
(explorer, artha),
(explorer, dharma),
(explorer, kama),
(explorer, moksha),
(killer, artha),
(killer, dharma),
(killer, kama),
(killer, moksha),
(socializer, artha),
(socializer, dharma),
(socializer, kama),
(socializer, moksha) }
Bartle taxonomy of player types