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
$$A \cup B =$$
{ antithesis, committee, ecology, hierarchy, matrix, synthesis, thesis }
Symmetric Difference
$$A \ominus B =$$
{ antithesis, committee, ecology, hierarchy, matrix, synthesis, thesis }
Difference
$$A - B =$$
{ antithesis, synthesis, thesis }
Difference
$$B - A =$$
{ committee, ecology, hierarchy, matrix }
Cartesian Product
$$A \times B =$$
{ (antithesis, committee),
(antithesis, ecology),
(antithesis, hierarchy),
(antithesis, matrix),
(synthesis, committee),
(synthesis, ecology),
(synthesis, hierarchy),
(synthesis, matrix),
(thesis, committee),
(thesis, ecology),
(thesis, hierarchy),
(thesis, matrix) }
Georg Wilhelm Friedrich Hegel