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, metal, metaphysics, normative science, phenomenology, water, wood }
Symmetric Difference
$$A \ominus B =$$
{ earth, fire, metal, metaphysics, normative science, phenomenology, water, wood }
Difference
$$A - B =$$
{ earth, fire, metal, water, wood }
Difference
$$B - A =$$
{ metaphysics, normative science, phenomenology }
Cartesian Product
$$A \times B =$$
{ (earth, metaphysics),
(earth, normative science),
(earth, phenomenology),
(fire, metaphysics),
(fire, normative science),
(fire, phenomenology),
(metal, metaphysics),
(metal, normative science),
(metal, phenomenology),
(water, metaphysics),
(water, normative science),
(water, phenomenology),
(wood, metaphysics),
(wood, normative science),
(wood, phenomenology) }
Charles Sanders Peirce