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
$$A \cup B =$$
{ avoiding, conduct, faith, getting, knowledge, ruling, socially useful }
Symmetric Difference
$$A \ominus B =$$
{ avoiding, conduct, faith, getting, knowledge, ruling, socially useful }
Difference
$$A - B =$$
{ conduct, faith, knowledge }
Difference
$$B - A =$$
{ avoiding, getting, ruling, socially useful }
Cartesian Product
$$A \times B =$$
{ (conduct, avoiding),
(conduct, getting),
(conduct, ruling),
(conduct, socially useful),
(faith, avoiding),
(faith, getting),
(faith, ruling),
(faith, socially useful),
(knowledge, avoiding),
(knowledge, getting),
(knowledge, ruling),
(knowledge, socially useful) }