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
$$A \cup B =$$
{ forming, hope, norming, performing, pray, repeat if necessary, storming }
Symmetric Difference
$$A \ominus B =$$
{ forming, hope, norming, performing, pray, repeat if necessary, storming }
Difference
$$A - B =$$
{ forming, norming, performing, storming }
Difference
$$B - A =$$
{ hope, pray, repeat if necessary }
Cartesian Product
$$A \times B =$$
{ (forming, hope),
(forming, pray),
(forming, repeat if necessary),
(norming, hope),
(norming, pray),
(norming, repeat if necessary),
(performing, hope),
(performing, pray),
(performing, repeat if necessary),
(storming, hope),
(storming, pray),
(storming, repeat if necessary) }