Union
$$A \cup B =$$
{ declarative, earth, exclamatory, fire, imperative, interrogative, void, water, wind }
Symmetric Difference
$$A \ominus B =$$
{ declarative, earth, exclamatory, fire, imperative, interrogative, void, water, wind }
Difference
$$A - B =$$
{ earth, fire, void, water, wind }
Difference
$$B - A =$$
{ declarative, exclamatory, imperative, interrogative }
Cartesian Product
$$A \times B =$$
{ (earth, declarative),
(earth, exclamatory),
(earth, imperative),
(earth, interrogative),
(fire, declarative),
(fire, exclamatory),
(fire, imperative),
(fire, interrogative),
(void, declarative),
(void, exclamatory),
(void, imperative),
(void, interrogative),
(water, declarative),
(water, exclamatory),
(water, imperative),
(water, interrogative),
(wind, declarative),
(wind, exclamatory),
(wind, imperative),
(wind, interrogative) }
Five elements (Japanese philosophy)