Equality
$$A \neq B$$
A is not equal to B
Subset
$$A \not\subseteq B$$
A is not a subset of or equal to B
Superset
$$A \not\supseteq B$$
A is not a superset of or equal to B
Intersection
$$A \cap B =$$
{ }
Union
$$A \cup B =$$
{ aesthetics, aristocracy, democracy, ethics, logic, oligarchy, timocracy, tyranny }
Symmetric Difference
$$A \ominus B =$$
{ aesthetics, aristocracy, democracy, ethics, logic, oligarchy, timocracy, tyranny }
Difference
$$A - B =$$
{ aristocracy, democracy, oligarchy, timocracy, tyranny }
Difference
$$B - A =$$
{ aesthetics, ethics, logic }
Cartesian Product
$$A \times B =$$
{ (aristocracy, aesthetics),
(aristocracy, ethics),
(aristocracy, logic),
(democracy, aesthetics),
(democracy, ethics),
(democracy, logic),
(oligarchy, aesthetics),
(oligarchy, ethics),
(oligarchy, logic),
(timocracy, aesthetics),
(timocracy, ethics),
(timocracy, logic),
(tyranny, aesthetics),
(tyranny, ethics),
(tyranny, logic) }
Charles Sanders Peirce