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
$$A \cup B =$$
{ enclosure, hearth, liberty, life, mound, pursuit of happiness, roof }
Symmetric Difference
$$A \ominus B =$$
{ enclosure, hearth, liberty, life, mound, pursuit of happiness, roof }
Difference
$$A - B =$$
{ enclosure, hearth, mound, roof }
Difference
$$B - A =$$
{ liberty, life, pursuit of happiness }
Cartesian Product
$$A \times B =$$
{ (enclosure, liberty),
(enclosure, life),
(enclosure, pursuit of happiness),
(hearth, liberty),
(hearth, life),
(hearth, pursuit of happiness),
(mound, liberty),
(mound, life),
(mound, pursuit of happiness),
(roof, liberty),
(roof, life),
(roof, pursuit of happiness) }