Union
$$A \cup B =$$
{ achiever, critic, enthusiast, helper, interpretant, loyalist, mediator, object, observer, protector, romantic, sign }
Symmetric Difference
$$A \ominus B =$$
{ achiever, critic, enthusiast, helper, interpretant, loyalist, mediator, object, observer, protector, romantic, sign }
Difference
$$A - B =$$
{ achiever, critic, enthusiast, helper, loyalist, mediator, observer, protector, romantic }
Cartesian Product
$$A \times B =$$
{ (achiever, interpretant),
(achiever, object),
(achiever, sign),
(critic, interpretant),
(critic, object),
(critic, sign),
(enthusiast, interpretant),
(enthusiast, object),
(enthusiast, sign),
(helper, interpretant),
(helper, object),
(helper, sign),
(loyalist, interpretant),
(loyalist, object),
(loyalist, sign),
(mediator, interpretant),
(mediator, object),
(mediator, sign),
(observer, interpretant),
(observer, object),
(observer, sign),
(protector, interpretant),
(protector, object),
(protector, sign),
(romantic, interpretant),
(romantic, object),
(romantic, sign) }