Union
$$A \cup B =$$
{ aristocracy, democracy, efficient (creator), final (function), formal (design), material, oligarchy, timocracy, tyranny }
Symmetric Difference
$$A \ominus B =$$
{ aristocracy, democracy, efficient (creator), final (function), formal (design), material, oligarchy, timocracy, tyranny }
Difference
$$A - B =$$
{ aristocracy, democracy, oligarchy, timocracy, tyranny }
Difference
$$B - A =$$
{ efficient (creator), final (function), formal (design), material }
Cartesian Product
$$A \times B =$$
{ (aristocracy, efficient (creator)),
(aristocracy, final (function)),
(aristocracy, formal (design)),
(aristocracy, material),
(democracy, efficient (creator)),
(democracy, final (function)),
(democracy, formal (design)),
(democracy, material),
(oligarchy, efficient (creator)),
(oligarchy, final (function)),
(oligarchy, formal (design)),
(oligarchy, material),
(timocracy, efficient (creator)),
(timocracy, final (function)),
(timocracy, formal (design)),
(timocracy, material),
(tyranny, efficient (creator)),
(tyranny, final (function)),
(tyranny, formal (design)),
(tyranny, material) }
Plato's five regimes