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
$$A \cup B =$$
{ arithmetic, astronomy, conscious competence, conscious incompetence, geometry, music, unconscious competence, unconscious incompetence }
Symmetric Difference
$$A \ominus B =$$
{ arithmetic, astronomy, conscious competence, conscious incompetence, geometry, music, unconscious competence, unconscious incompetence }
Difference
$$A - B =$$
{ arithmetic, astronomy, geometry, music }
Difference
$$B - A =$$
{ conscious competence, conscious incompetence, unconscious competence, unconscious incompetence }
Cartesian Product
$$A \times B =$$
{ (arithmetic, conscious competence),
(arithmetic, conscious incompetence),
(arithmetic, unconscious competence),
(arithmetic, unconscious incompetence),
(astronomy, conscious competence),
(astronomy, conscious incompetence),
(astronomy, unconscious competence),
(astronomy, unconscious incompetence),
(geometry, conscious competence),
(geometry, conscious incompetence),
(geometry, unconscious competence),
(geometry, unconscious incompetence),
(music, conscious competence),
(music, conscious incompetence),
(music, unconscious competence),
(music, unconscious incompetence) }
Four stages of competence