Union
$$A \cup B =$$
{ achiever, auditory, explorer, killer, physical, social, socializer, visual }
Symmetric Difference
$$A \ominus B =$$
{ achiever, auditory, explorer, killer, physical, social, socializer, visual }
Difference
$$A - B =$$
{ achiever, explorer, killer, socializer }
Difference
$$B - A =$$
{ auditory, physical, social, visual }
Cartesian Product
$$A \times B =$$
{ (achiever, auditory),
(achiever, physical),
(achiever, social),
(achiever, visual),
(explorer, auditory),
(explorer, physical),
(explorer, social),
(explorer, visual),
(killer, auditory),
(killer, physical),
(killer, social),
(killer, visual),
(socializer, auditory),
(socializer, physical),
(socializer, social),
(socializer, visual) }
Bartle taxonomy of player types