Self-study
Not surprisingly, there are no professors under the age of eighteen. ████ ██ ██ ████ ██████ ██ ███ █████ ████████ ███ ████ ████████ ████████ ████ █████████ ██████ ███ ███████████ ████ ███ █████ ███████ ███ ████ ███ █████ █████████
Summary
The stimulus can be diagrammed as follows:
Notable Valid Inferences
Some brilliant people are not professors.
Some brilliant people cannot legally vote.
11.
If the statements above are █████ ████ ██ ███ █████ ██ ████ █████ ███ ██ ███ █████████ ████ ████ ██ █████
a
No professors are ███████████████████
Could be false. Some professors could be eighteen-year-olds. We know that no professors are under eighteen, but this leaves room for the possibility that some professors are exactly eighteen.
b
All brilliant people ███ ██████ ███████████ █████ ███████ ██ █████ █████████
Could be false. We know that some brilliant people are professors, legal voters, and/or under eighteen. But this may not be an exhaustive list. There could be brilliant people out there who are none of these three things.
c
Some legal voters ███ ███ ███████████
Could be false. It’s possible that all legal voters are professors. The only things we can say for sure about legal voters are that some of them are brilliant people, and none of them are under eighteen.
d
Some professors are ███████ █████ ██████ ███ █████████ ███████
Could be false. It’s possible that all professors are either legal voters or brilliant people, or both. The only things we can say for sure about professors are that at least some of them are brilliant people, and none of them are under eighteen.
e
Some brilliant people ███ ███████ ██████████ ███ █████ ███████
Must be true. Some brilliant people are under eighteen, meaning they are not professors and cannot legally vote.