Equality
$$A \neq B$$
A is not equal to B
Subset
$$A \not\subseteq B$$
A is not a subset of or equal to B
Superset
$$A \not\supseteq B$$
A is not a superset of or equal to B
Intersection
$$A \cap B =$$
{ }
Union
$$A \cup B =$$
{ earth, fire, galactic, planetary, stellar, void, water, wind }
Symmetric Difference
$$A \ominus B =$$
{ earth, fire, galactic, planetary, stellar, void, water, wind }
Difference
$$A - B =$$
{ galactic, planetary, stellar }
Difference
$$B - A =$$
{ earth, fire, void, water, wind }
Cartesian Product
$$A \times B =$$
{ (galactic, earth),
(galactic, fire),
(galactic, void),
(galactic, water),
(galactic, wind),
(planetary, earth),
(planetary, fire),
(planetary, void),
(planetary, water),
(planetary, wind),
(stellar, earth),
(stellar, fire),
(stellar, void),
(stellar, water),
(stellar, wind) }
Kardashev scale