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
$$A \cup B =$$
{ air, antithesis, earth, fire, synthesis, thesis, vegetable, water }
Symmetric Difference
$$A \ominus B =$$
{ air, antithesis, earth, fire, synthesis, thesis, vegetable, water }
Difference
$$A - B =$$
{ air, earth, fire, vegetable, water }
Difference
$$B - A =$$
{ antithesis, synthesis, thesis }
Cartesian Product
$$A \times B =$$
{ (air, antithesis),
(air, synthesis),
(air, thesis),
(earth, antithesis),
(earth, synthesis),
(earth, thesis),
(fire, antithesis),
(fire, synthesis),
(fire, thesis),
(vegetable, antithesis),
(vegetable, synthesis),
(vegetable, thesis),
(water, antithesis),
(water, synthesis),
(water, thesis) }
Georg Wilhelm Friedrich Hegel