Not surprisingly, there are no professors under the age of eighteen. And, as well known, no one under eighteen can v...

BenMingov on April 9, 2020

Hi Gharibiannick, thanks for the question.

This passage provides us with two conditions and three quantifier statements.

There are no professors under the age of eighteen (Professor -> Not under age of 18) -- contrapositive (Under age of 18 -> Not Professor)

No one under eighteen can vote legally (Under age of 18 -> Not vote legally) -- contrapositive (Vote legally -> Not under age of 18)

Some brilliant people are professors (Brilliant people <-some-> Professors)

Some brilliant people are legal voters (Brilliant people <-some-> vote legally)

Some brilliant people are under eighteen (Brilliant people <-some-> under age of 18)


Granted, if you were to do this during a timed test, then you would abbreviate your conditions. But I am just expanding them so that everything is clearly labelled.

Now we are to find what must be true based on these conditions.

A) No professors are eighteen year olds. (Professor -> Not 18)

How can we be sure that no professors are exactly 18. All we know is that none are under 18.

B) All brilliant people are either professors, legal voters, or under eighteen. (Brilliant people -> Professor or Vote Legally or Under 18)

There is nothing in the passage that makes this true. It is possible that someone who is brilliant is none of these things.

C) Some legal voters are not professors. (Vote legally <-some-> Not Professors)

Again, there is no way to add up the statements in order to come about the inference that some who can vote legally are not professors.

D) Some professors are neither legal voters nor brilliant people (Professors <-some-> Not vote legally and Not Brilliant people)

We cannot deduce this from the combination of any statements.

E) Some brilliant people are neither professors nor legal voters (Brilliant people <-some-> Not professor and Not legal voters)

This comes from combining the following:

Brilliant people <-some-> under age of 18 combined with both

Under age of 18 -> Not Professor

And

Under age of 18 -> Not vote legally

I hope this helps. Please let me know if you have any other questions.