Union
$$A \cup B =$$
{ charismatic authority, electric, fossil, gravitational, hydric, legal authority, organic, solar, thermal, traditional authority, wind }
Symmetric Difference
$$A \ominus B =$$
{ charismatic authority, electric, fossil, gravitational, hydric, legal authority, organic, solar, thermal, traditional authority, wind }
Difference
$$B - A =$$
{ electric, fossil, gravitational, hydric, organic, solar, thermal, wind }
Cartesian Product
$$A \times B =$$
{ (charismatic authority, electric),
(charismatic authority, fossil),
(charismatic authority, gravitational),
(charismatic authority, hydric),
(charismatic authority, organic),
(charismatic authority, solar),
(charismatic authority, thermal),
(charismatic authority, wind),
(legal authority, electric),
(legal authority, fossil),
(legal authority, gravitational),
(legal authority, hydric),
(legal authority, organic),
(legal authority, solar),
(legal authority, thermal),
(legal authority, wind),
(traditional authority, electric),
(traditional authority, fossil),
(traditional authority, gravitational),
(traditional authority, hydric),
(traditional authority, organic),
(traditional authority, solar),
(traditional authority, thermal),
(traditional authority, wind) }
The Three Types of Legitimate Rule