Union
$$A \cup B =$$
{ earth, grass, heaven, interval, lake, mountain, nominal, ordinal, ratio, river, thunder, wood }
Symmetric Difference
$$A \ominus B =$$
{ earth, grass, heaven, interval, lake, mountain, nominal, ordinal, ratio, river, thunder, wood }
Difference
$$B - A =$$
{ earth, grass, heaven, lake, mountain, river, thunder, wood }
Cartesian Product
$$A \times B =$$
{ (interval, earth),
(interval, grass),
(interval, heaven),
(interval, lake),
(interval, mountain),
(interval, river),
(interval, thunder),
(interval, wood),
(nominal, earth),
(nominal, grass),
(nominal, heaven),
(nominal, lake),
(nominal, mountain),
(nominal, river),
(nominal, thunder),
(nominal, wood),
(ordinal, earth),
(ordinal, grass),
(ordinal, heaven),
(ordinal, lake),
(ordinal, mountain),
(ordinal, river),
(ordinal, thunder),
(ordinal, wood),
(ratio, earth),
(ratio, grass),
(ratio, heaven),
(ratio, lake),
(ratio, mountain),
(ratio, river),
(ratio, thunder),
(ratio, wood) }
Level of measurement