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
$$A \cup B =$$
{ awareness, context-free, context-sensitive, decision, recognition, recollection, recursively enumerable, regular }
Symmetric Difference
$$A \ominus B =$$
{ awareness, context-free, context-sensitive, decision, recognition, recollection, recursively enumerable, regular }
Difference
$$A - B =$$
{ context-free, context-sensitive, recursively enumerable, regular }
Difference
$$B - A =$$
{ awareness, decision, recognition, recollection }
Cartesian Product
$$A \times B =$$
{ (context-free, awareness),
(context-free, decision),
(context-free, recognition),
(context-free, recollection),
(context-sensitive, awareness),
(context-sensitive, decision),
(context-sensitive, recognition),
(context-sensitive, recollection),
(recursively enumerable, awareness),
(recursively enumerable, decision),
(recursively enumerable, recognition),
(recursively enumerable, recollection),
(regular, awareness),
(regular, decision),
(regular, recognition),
(regular, recollection) }
Chomsky hierarchy