Scott - Near the top of your explanation, after the second diagram, you wrote:

Each of Product Managers, Engineers and Mathematicians has at least one person in it. So there are no non-empty subsets.

Change non-empty --> empty? (I'm not suggesting that non-empty is finer than empty. :-) )

Each of Product Managers, Engineers and Mathematicians has at least one person in it. So there are no non-empty subsets.

Change non-empty --> empty? (I'm not suggesting that non-empty is finer than empty. :-) )