Union
$$A \cup B =$$
{ context-free, context-sensitive, forward/back, left/right, pitch, recursively enumerable, regular, roll, up/down, yaw }
Symmetric Difference
$$A \ominus B =$$
{ context-free, context-sensitive, forward/back, left/right, pitch, recursively enumerable, regular, roll, up/down, yaw }
Difference
$$B - A =$$
{ forward/back, left/right, pitch, roll, up/down, yaw }
Cartesian Product
$$A \times B =$$
{ (context-free, forward/back),
(context-free, left/right),
(context-free, pitch),
(context-free, roll),
(context-free, up/down),
(context-free, yaw),
(context-sensitive, forward/back),
(context-sensitive, left/right),
(context-sensitive, pitch),
(context-sensitive, roll),
(context-sensitive, up/down),
(context-sensitive, yaw),
(recursively enumerable, forward/back),
(recursively enumerable, left/right),
(recursively enumerable, pitch),
(recursively enumerable, roll),
(recursively enumerable, up/down),
(recursively enumerable, yaw),
(regular, forward/back),
(regular, left/right),
(regular, pitch),
(regular, roll),
(regular, up/down),
(regular, yaw) }