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
$$A \cup B =$$
{ critical, earth, fire, metal, speculative grammar, speculative rhetoric, water, wood }
Symmetric Difference
$$A \ominus B =$$
{ critical, earth, fire, metal, speculative grammar, speculative rhetoric, water, wood }
Difference
$$A - B =$$
{ critical, speculative grammar, speculative rhetoric }
Difference
$$B - A =$$
{ earth, fire, metal, water, wood }
Cartesian Product
$$A \times B =$$
{ (critical, earth),
(critical, fire),
(critical, metal),
(critical, water),
(critical, wood),
(speculative grammar, earth),
(speculative grammar, fire),
(speculative grammar, metal),
(speculative grammar, water),
(speculative grammar, wood),
(speculative rhetoric, earth),
(speculative rhetoric, fire),
(speculative rhetoric, metal),
(speculative rhetoric, water),
(speculative rhetoric, wood) }
Charles Sanders Peirce