Union
$$A \cup B =$$
{ context-free, context-sensitive, covetousness, frivolous talk, ill will, killing, lying, recursively enumerable, regular, rude speech, sexual misconduct, slandering, stealing, wrong view }
Symmetric Difference
$$A \ominus B =$$
{ context-free, context-sensitive, covetousness, frivolous talk, ill will, killing, lying, recursively enumerable, regular, rude speech, sexual misconduct, slandering, stealing, wrong view }
Cartesian Product
$$A \times B =$$
{ (covetousness, context-free),
(covetousness, context-sensitive),
(covetousness, recursively enumerable),
(covetousness, regular),
(frivolous talk, context-free),
(frivolous talk, context-sensitive),
(frivolous talk, recursively enumerable),
(frivolous talk, regular),
(ill will, context-free),
(ill will, context-sensitive),
(ill will, recursively enumerable),
(ill will, regular),
(killing, context-free),
(killing, context-sensitive),
(killing, recursively enumerable),
(killing, regular),
(lying, context-free),
(lying, context-sensitive),
(lying, recursively enumerable),
(lying, regular),
(rude speech, context-free),
(rude speech, context-sensitive),
(rude speech, recursively enumerable),
(rude speech, regular),
(sexual misconduct, context-free),
(sexual misconduct, context-sensitive),
(sexual misconduct, recursively enumerable),
(sexual misconduct, regular),
(slandering, context-free),
(slandering, context-sensitive),
(slandering, recursively enumerable),
(slandering, regular),
(stealing, context-free),
(stealing, context-sensitive),
(stealing, recursively enumerable),
(stealing, regular),
(wrong view, context-free),
(wrong view, context-sensitive),
(wrong view, recursively enumerable),
(wrong view, regular) }
Chomsky hierarchy