Union
$$A \cup B =$$
{ called, common, context-free, context-sensitive, holy sage, recursively enumerable, regular, superior, worthy }
Symmetric Difference
$$A \ominus B =$$
{ called, common, context-free, context-sensitive, holy sage, recursively enumerable, regular, superior, worthy }
Difference
$$A - B =$$
{ context-free, context-sensitive, recursively enumerable, regular }
Difference
$$B - A =$$
{ called, common, holy sage, superior, worthy }
Cartesian Product
$$A \times B =$$
{ (context-free, called),
(context-free, common),
(context-free, holy sage),
(context-free, superior),
(context-free, worthy),
(context-sensitive, called),
(context-sensitive, common),
(context-sensitive, holy sage),
(context-sensitive, superior),
(context-sensitive, worthy),
(recursively enumerable, called),
(recursively enumerable, common),
(recursively enumerable, holy sage),
(recursively enumerable, superior),
(recursively enumerable, worthy),
(regular, called),
(regular, common),
(regular, holy sage),
(regular, superior),
(regular, worthy) }
Chomsky hierarchy