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
$$A \cup B =$$
{ conduct, earth, faith, fire, knowledge, void, water, wind }
Symmetric Difference
$$A \ominus B =$$
{ conduct, earth, faith, fire, knowledge, void, water, wind }
Difference
$$A - B =$$
{ earth, fire, void, water, wind }
Difference
$$B - A =$$
{ conduct, faith, knowledge }
Cartesian Product
$$A \times B =$$
{ (earth, conduct),
(earth, faith),
(earth, knowledge),
(fire, conduct),
(fire, faith),
(fire, knowledge),
(void, conduct),
(void, faith),
(void, knowledge),
(water, conduct),
(water, faith),
(water, knowledge),
(wind, conduct),
(wind, faith),
(wind, knowledge) }