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, knowledge, position, status, void, water, wind }
Symmetric Difference
$$A \ominus B =$$
{ earth, fire, knowledge, position, status, void, water, wind }
Difference
$$A - B =$$
{ knowledge, position, status }
Difference
$$B - A =$$
{ earth, fire, void, water, wind }
Cartesian Product
$$A \times B =$$
{ (knowledge, earth),
(knowledge, fire),
(knowledge, void),
(knowledge, water),
(knowledge, wind),
(position, earth),
(position, fire),
(position, void),
(position, water),
(position, wind),
(status, earth),
(status, fire),
(status, void),
(status, water),
(status, wind) }
Authority (sociology)