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