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
$$A \cup B =$$
{ failed, interpretant, object, physical, psychic, sign, successful }
Symmetric Difference
$$A \ominus B =$$
{ failed, interpretant, object, physical, psychic, sign, successful }
Difference
$$A - B =$$
{ interpretant, object, sign }
Difference
$$B - A =$$
{ failed, physical, psychic, successful }
Cartesian Product
$$A \times B =$$
{ (interpretant, failed),
(interpretant, physical),
(interpretant, psychic),
(interpretant, successful),
(object, failed),
(object, physical),
(object, psychic),
(object, successful),
(sign, failed),
(sign, physical),
(sign, psychic),
(sign, successful) }
Semiotic theory of Charles Sanders Peirce