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, hope, physical, pray, psychic, repeat if necessary, successful }
Symmetric Difference
$$A \ominus B =$$
{ failed, hope, physical, pray, psychic, repeat if necessary, successful }
Difference
$$A - B =$$
{ hope, pray, repeat if necessary }
Difference
$$B - A =$$
{ failed, physical, psychic, successful }
Cartesian Product
$$A \times B =$$
{ (hope, failed),
(hope, physical),
(hope, psychic),
(hope, successful),
(pray, failed),
(pray, physical),
(pray, psychic),
(pray, successful),
(repeat if necessary, failed),
(repeat if necessary, physical),
(repeat if necessary, psychic),
(repeat if necessary, successful) }
Salvation