Union
$$A \cup B =$$
{ archery, calligraphy, chariotry, gemini, mathematics, music, pisces, rites, sagittarius, virgo }
Symmetric Difference
$$A \ominus B =$$
{ archery, calligraphy, chariotry, gemini, mathematics, music, pisces, rites, sagittarius, virgo }
Difference
$$A - B =$$
{ archery, calligraphy, chariotry, mathematics, music, rites }
Cartesian Product
$$A \times B =$$
{ (archery, gemini),
(archery, pisces),
(archery, sagittarius),
(archery, virgo),
(calligraphy, gemini),
(calligraphy, pisces),
(calligraphy, sagittarius),
(calligraphy, virgo),
(chariotry, gemini),
(chariotry, pisces),
(chariotry, sagittarius),
(chariotry, virgo),
(mathematics, gemini),
(mathematics, pisces),
(mathematics, sagittarius),
(mathematics, virgo),
(music, gemini),
(music, pisces),
(music, sagittarius),
(music, virgo),
(rites, gemini),
(rites, pisces),
(rites, sagittarius),
(rites, virgo) }