Union
$$A \cup B =$$
{ arithmetic, astronomy, geometry, glide reflection, music, reflection, rotation, translation }
Symmetric Difference
$$A \ominus B =$$
{ arithmetic, astronomy, geometry, glide reflection, music, reflection, rotation, translation }
Difference
$$A - B =$$
{ arithmetic, astronomy, geometry, music }
Difference
$$B - A =$$
{ glide reflection, reflection, rotation, translation }
Cartesian Product
$$A \times B =$$
{ (arithmetic, glide reflection),
(arithmetic, reflection),
(arithmetic, rotation),
(arithmetic, translation),
(astronomy, glide reflection),
(astronomy, reflection),
(astronomy, rotation),
(astronomy, translation),
(geometry, glide reflection),
(geometry, reflection),
(geometry, rotation),
(geometry, translation),
(music, glide reflection),
(music, reflection),
(music, rotation),
(music, translation) }
Quadrivium