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
$$A \cup B =$$
{ ambiguities, distortion, fiction, hope, paradox, pray, repeat if necessary }
Symmetric Difference
$$A \ominus B =$$
{ ambiguities, distortion, fiction, hope, paradox, pray, repeat if necessary }
Difference
$$A - B =$$
{ hope, pray, repeat if necessary }
Difference
$$B - A =$$
{ ambiguities, distortion, fiction, paradox }
Cartesian Product
$$A \times B =$$
{ (hope, ambiguities),
(hope, distortion),
(hope, fiction),
(hope, paradox),
(pray, ambiguities),
(pray, distortion),
(pray, fiction),
(pray, paradox),
(repeat if necessary, ambiguities),
(repeat if necessary, distortion),
(repeat if necessary, fiction),
(repeat if necessary, paradox) }