Union
$$A \cup B =$$
{ earth, fire, interval, nominal, ordinal, ratio, void, water, wind }
Symmetric Difference
$$A \ominus B =$$
{ earth, fire, interval, nominal, ordinal, ratio, void, water, wind }
Difference
$$A - B =$$
{ interval, nominal, ordinal, ratio }
Difference
$$B - A =$$
{ earth, fire, void, water, wind }
Cartesian Product
$$A \times B =$$
{ (interval, earth),
(interval, fire),
(interval, void),
(interval, water),
(interval, wind),
(nominal, earth),
(nominal, fire),
(nominal, void),
(nominal, water),
(nominal, wind),
(ordinal, earth),
(ordinal, fire),
(ordinal, void),
(ordinal, water),
(ordinal, wind),
(ratio, earth),
(ratio, fire),
(ratio, void),
(ratio, water),
(ratio, wind) }
Level of measurement