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
$$A \cup B =$$
{ air, earth, fire, metaphysical, positivity, theological, water }
Symmetric Difference
$$A \ominus B =$$
{ air, earth, fire, metaphysical, positivity, theological, water }
Difference
$$A - B =$$
{ metaphysical, positivity, theological }
Difference
$$B - A =$$
{ air, earth, fire, water }
Cartesian Product
$$A \times B =$$
{ (metaphysical, air),
(metaphysical, earth),
(metaphysical, fire),
(metaphysical, water),
(positivity, air),
(positivity, earth),
(positivity, fire),
(positivity, water),
(theological, air),
(theological, earth),
(theological, fire),
(theological, water) }