Union
$$A \cup B =$$
{ agent, form, gemini, matter, pisces, purpose, sagittarius, virgo }
Symmetric Difference
$$A \ominus B =$$
{ agent, form, gemini, matter, pisces, purpose, sagittarius, virgo }
Difference
$$A - B =$$
{ gemini, pisces, sagittarius, virgo }
Difference
$$B - A =$$
{ agent, form, matter, purpose }
Cartesian Product
$$A \times B =$$
{ (gemini, agent),
(gemini, form),
(gemini, matter),
(gemini, purpose),
(pisces, agent),
(pisces, form),
(pisces, matter),
(pisces, purpose),
(sagittarius, agent),
(sagittarius, form),
(sagittarius, matter),
(sagittarius, purpose),
(virgo, agent),
(virgo, form),
(virgo, matter),
(virgo, purpose) }