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
$$A \cup B =$$
{ angry, bored, happy, liberty, life, peaceful, pursuit of happiness }
Symmetric Difference
$$A \ominus B =$$
{ angry, bored, happy, liberty, life, peaceful, pursuit of happiness }
Difference
$$A - B =$$
{ liberty, life, pursuit of happiness }
Difference
$$B - A =$$
{ angry, bored, happy, peaceful }
Cartesian Product
$$A \times B =$$
{ (liberty, angry),
(liberty, bored),
(liberty, happy),
(liberty, peaceful),
(life, angry),
(life, bored),
(life, happy),
(life, peaceful),
(pursuit of happiness, angry),
(pursuit of happiness, bored),
(pursuit of happiness, happy),
(pursuit of happiness, peaceful) }