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
$$A \cup B =$$
{ animal, heaven, hell, knowledge, plant, position, status }
Symmetric Difference
$$A \ominus B =$$
{ animal, heaven, hell, knowledge, plant, position, status }
Difference
$$A - B =$$
{ knowledge, position, status }
Difference
$$B - A =$$
{ animal, heaven, hell, plant }
Cartesian Product
$$A \times B =$$
{ (knowledge, animal),
(knowledge, heaven),
(knowledge, hell),
(knowledge, plant),
(position, animal),
(position, heaven),
(position, hell),
(position, plant),
(status, animal),
(status, heaven),
(status, hell),
(status, plant) }