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
$$A \cup B =$$
{ agent, form, hope, matter, pray, purpose, repeat if necessary }
Symmetric Difference
$$A \ominus B =$$
{ agent, form, hope, matter, pray, purpose, repeat if necessary }
Difference
$$A - B =$$
{ hope, pray, repeat if necessary }
Difference
$$B - A =$$
{ agent, form, matter, purpose }
Cartesian Product
$$A \times B =$$
{ (hope, agent),
(hope, form),
(hope, matter),
(hope, purpose),
(pray, agent),
(pray, form),
(pray, matter),
(pray, purpose),
(repeat if necessary, agent),
(repeat if necessary, form),
(repeat if necessary, matter),
(repeat if necessary, purpose) }