Union
$$A \cup B =$$
{ achiever, explorer, killer, socializer, to not commit adultery, to not intoxicate, to not kill, to not lie, to not steal }
Symmetric Difference
$$A \ominus B =$$
{ achiever, explorer, killer, socializer, to not commit adultery, to not intoxicate, to not kill, to not lie, to not steal }
Difference
$$A - B =$$
{ achiever, explorer, killer, socializer }
Difference
$$B - A =$$
{ to not commit adultery, to not intoxicate, to not kill, to not lie, to not steal }
Cartesian Product
$$A \times B =$$
{ (achiever, to not commit adultery),
(achiever, to not intoxicate),
(achiever, to not kill),
(achiever, to not lie),
(achiever, to not steal),
(explorer, to not commit adultery),
(explorer, to not intoxicate),
(explorer, to not kill),
(explorer, to not lie),
(explorer, to not steal),
(killer, to not commit adultery),
(killer, to not intoxicate),
(killer, to not kill),
(killer, to not lie),
(killer, to not steal),
(socializer, to not commit adultery),
(socializer, to not intoxicate),
(socializer, to not kill),
(socializer, to not lie),
(socializer, to not steal) }