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
$$A \cup B =$$
{ critical, enclosure, hearth, mound, roof, speculative grammar, speculative rhetoric }
Symmetric Difference
$$A \ominus B =$$
{ critical, enclosure, hearth, mound, roof, speculative grammar, speculative rhetoric }
Difference
$$A - B =$$
{ critical, speculative grammar, speculative rhetoric }
Difference
$$B - A =$$
{ enclosure, hearth, mound, roof }
Cartesian Product
$$A \times B =$$
{ (critical, enclosure),
(critical, hearth),
(critical, mound),
(critical, roof),
(speculative grammar, enclosure),
(speculative grammar, hearth),
(speculative grammar, mound),
(speculative grammar, roof),
(speculative rhetoric, enclosure),
(speculative rhetoric, hearth),
(speculative rhetoric, mound),
(speculative rhetoric, roof) }
Charles Sanders Peirce