Union
$$A \cup B =$$
{ context-free, context-sensitive, enclosure, hearth, mound, recursively enumerable, regular, roof }
Symmetric Difference
$$A \ominus B =$$
{ context-free, context-sensitive, enclosure, hearth, mound, recursively enumerable, regular, roof }
Difference
$$A - B =$$
{ enclosure, hearth, mound, roof }
Difference
$$B - A =$$
{ context-free, context-sensitive, recursively enumerable, regular }
Cartesian Product
$$A \times B =$$
{ (enclosure, context-free),
(enclosure, context-sensitive),
(enclosure, recursively enumerable),
(enclosure, regular),
(hearth, context-free),
(hearth, context-sensitive),
(hearth, recursively enumerable),
(hearth, regular),
(mound, context-free),
(mound, context-sensitive),
(mound, recursively enumerable),
(mound, regular),
(roof, context-free),
(roof, context-sensitive),
(roof, recursively enumerable),
(roof, regular) }
Chomsky hierarchy