Union
$$A \cup B =$$
{ argument, dicent indexical legisign, dicent sinsign, dicent symbol, earth, fire, iconic legisign, iconic sinsign, metal, qualisign, rhematic indexical, rhematic indexical legisign, rhematic symbol, water, wood }
Symmetric Difference
$$A \ominus B =$$
{ argument, dicent indexical legisign, dicent sinsign, dicent symbol, earth, fire, iconic legisign, iconic sinsign, metal, qualisign, rhematic indexical, rhematic indexical legisign, rhematic symbol, water, wood }
Cartesian Product
$$A \times B =$$
{ (earth, argument),
(earth, dicent indexical legisign),
(earth, dicent sinsign),
(earth, dicent symbol),
(earth, iconic legisign),
(earth, iconic sinsign),
(earth, qualisign),
(earth, rhematic indexical),
(earth, rhematic indexical legisign),
(earth, rhematic symbol),
(fire, argument),
(fire, dicent indexical legisign),
(fire, dicent sinsign),
(fire, dicent symbol),
(fire, iconic legisign),
(fire, iconic sinsign),
(fire, qualisign),
(fire, rhematic indexical),
(fire, rhematic indexical legisign),
(fire, rhematic symbol),
(metal, argument),
(metal, dicent indexical legisign),
(metal, dicent sinsign),
(metal, dicent symbol),
(metal, iconic legisign),
(metal, iconic sinsign),
(metal, qualisign),
(metal, rhematic indexical),
(metal, rhematic indexical legisign),
(metal, rhematic symbol),
(water, argument),
(water, dicent indexical legisign),
(water, dicent sinsign),
(water, dicent symbol),
(water, iconic legisign),
(water, iconic sinsign),
(water, qualisign),
(water, rhematic indexical),
(water, rhematic indexical legisign),
(water, rhematic symbol),
(wood, argument),
(wood, dicent indexical legisign),
(wood, dicent sinsign),
(wood, dicent symbol),
(wood, iconic legisign),
(wood, iconic sinsign),
(wood, qualisign),
(wood, rhematic indexical),
(wood, rhematic indexical legisign),
(wood, rhematic symbol) }
Charles Sanders Peirce