Union
$$A \cup B =$$
{ class, family, genus, kingdom, matter, motion, order, phylum, rest, soul, space, species, time }
Symmetric Difference
$$A \ominus B =$$
{ class, family, genus, kingdom, matter, motion, order, phylum, rest, soul, space, species, time }
Cartesian Product
$$A \times B =$$
{ (class, matter),
(class, motion),
(class, rest),
(class, soul),
(class, space),
(class, time),
(family, matter),
(family, motion),
(family, rest),
(family, soul),
(family, space),
(family, time),
(genus, matter),
(genus, motion),
(genus, rest),
(genus, soul),
(genus, space),
(genus, time),
(kingdom, matter),
(kingdom, motion),
(kingdom, rest),
(kingdom, soul),
(kingdom, space),
(kingdom, time),
(order, matter),
(order, motion),
(order, rest),
(order, soul),
(order, space),
(order, time),
(phylum, matter),
(phylum, motion),
(phylum, rest),
(phylum, soul),
(phylum, space),
(phylum, time),
(species, matter),
(species, motion),
(species, rest),
(species, soul),
(species, space),
(species, time) }
Taxonomy (biology)