Union
$$A \cup B =$$
{ anal, context-free, context-sensitive, genital, latency, oral, phallic, recursively enumerable, regular }
Symmetric Difference
$$A \ominus B =$$
{ anal, context-free, context-sensitive, genital, latency, oral, phallic, recursively enumerable, regular }
Difference
$$A - B =$$
{ context-free, context-sensitive, recursively enumerable, regular }
Difference
$$B - A =$$
{ anal, genital, latency, oral, phallic }
Cartesian Product
$$A \times B =$$
{ (context-free, anal),
(context-free, genital),
(context-free, latency),
(context-free, oral),
(context-free, phallic),
(context-sensitive, anal),
(context-sensitive, genital),
(context-sensitive, latency),
(context-sensitive, oral),
(context-sensitive, phallic),
(recursively enumerable, anal),
(recursively enumerable, genital),
(recursively enumerable, latency),
(recursively enumerable, oral),
(recursively enumerable, phallic),
(regular, anal),
(regular, genital),
(regular, latency),
(regular, oral),
(regular, phallic) }
Chomsky hierarchy