Union
$$A \cup B =$$
{ deep sleep, dreaming, earth, fire, superconsciousness, void, waking, water, wind }
Symmetric Difference
$$A \ominus B =$$
{ deep sleep, dreaming, earth, fire, superconsciousness, void, waking, water, wind }
Difference
$$A - B =$$
{ earth, fire, void, water, wind }
Difference
$$B - A =$$
{ deep sleep, dreaming, superconsciousness, waking }
Cartesian Product
$$A \times B =$$
{ (earth, deep sleep),
(earth, dreaming),
(earth, superconsciousness),
(earth, waking),
(fire, deep sleep),
(fire, dreaming),
(fire, superconsciousness),
(fire, waking),
(void, deep sleep),
(void, dreaming),
(void, superconsciousness),
(void, waking),
(water, deep sleep),
(water, dreaming),
(water, superconsciousness),
(water, waking),
(wind, deep sleep),
(wind, dreaming),
(wind, superconsciousness),
(wind, waking) }