Union
$$A \cup B =$$
{ air, aquarius, earth, fire, leo, scorpio, taurus, water }
Symmetric Difference
$$A \ominus B =$$
{ air, aquarius, earth, fire, leo, scorpio, taurus, water }
Difference
$$A - B =$$
{ air, earth, fire, water }
Difference
$$B - A =$$
{ aquarius, leo, scorpio, taurus }
Cartesian Product
$$A \times B =$$
{ (air, aquarius),
(air, leo),
(air, scorpio),
(air, taurus),
(earth, aquarius),
(earth, leo),
(earth, scorpio),
(earth, taurus),
(fire, aquarius),
(fire, leo),
(fire, scorpio),
(fire, taurus),
(water, aquarius),
(water, leo),
(water, scorpio),
(water, taurus) }