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
$$A \cup B =$$
{ context-free, context-sensitive, metaphysical, positivity, recursively enumerable, regular, theological }
Symmetric Difference
$$A \ominus B =$$
{ context-free, context-sensitive, metaphysical, positivity, recursively enumerable, regular, theological }
Difference
$$A - B =$$
{ context-free, context-sensitive, recursively enumerable, regular }
Difference
$$B - A =$$
{ metaphysical, positivity, theological }
Cartesian Product
$$A \times B =$$
{ (context-free, metaphysical),
(context-free, positivity),
(context-free, theological),
(context-sensitive, metaphysical),
(context-sensitive, positivity),
(context-sensitive, theological),
(recursively enumerable, metaphysical),
(recursively enumerable, positivity),
(recursively enumerable, theological),
(regular, metaphysical),
(regular, positivity),
(regular, theological) }
Chomsky hierarchy