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
$$A \cup B =$$
{ darkness, earth, fire, goodness, metal, passion, water, wood }
Symmetric Difference
$$A \ominus B =$$
{ darkness, earth, fire, goodness, metal, passion, water, wood }
Difference
$$A - B =$$
{ darkness, goodness, passion }
Difference
$$B - A =$$
{ earth, fire, metal, water, wood }
Cartesian Product
$$A \times B =$$
{ (darkness, earth),
(darkness, fire),
(darkness, metal),
(darkness, water),
(darkness, wood),
(goodness, earth),
(goodness, fire),
(goodness, metal),
(goodness, water),
(goodness, wood),
(passion, earth),
(passion, fire),
(passion, metal),
(passion, water),
(passion, wood) }