#11 - Not surprisingly, there are no professors under the

[ellenb]

Dear Powerscore,

Please let me know how why E was picked to the right answer.

Stimulus: Professor->Not under 18
Under 18-->Not Vote Legally


Answer:

Briliant ppl some->not Professors and not Legal Voters

Please let me know whether I have diagrammed the stimulus and the answer correctly.

Regards,

Ellen

[Steve Stein]

Hi Ellen,

Good question, and you diagrammed the first part of the stimulus correctly, but you left out the contrapositives and the "some" rules. The author provides, as you point out, that if you are a professor, you are not under the age of 18.

Rule: Professor NOT under 18
Contrapositive: Under 18 NOT professor

Further, the author provides that if you are under 18, you cannot vote legally:

Rule: Under 18 NOT vote legally
Contrapositive: Vote legally NOT under 18

The author of the stimulus then closes with three separate "some" rules, which can be linked in each case to the rules from above:

some brilliant people are professors: BP Profs NOT under 18
some brilliant people are legal voters: BP vote legally NOT under 18

some brilliant people are under 18: BP under 18 NOT vote legally
(recall that those under 18 cant be professors): BP under 18 NOT professor

As we can see from the linked rules above, there are some brilliant people (those under 18) who are neither professors nor legal voters.

I hope that's helpful! Please let me know whether this is clear--thanks!

~Steve

[ellenb]

thanks a lot Steve!

Makes more sense, did you mean to put a some statement in the beginning of your some statements?


Also, if I diagram the answer, it should say,

BP some not Professors and not Legal Voters ?

Thanks

Ellen

[Steve Stein]

Hey Ellen,

Thanks for your response--that's exactly right.

~Steve

[Sherry001]

Hello ,
I had trouble diagramming parts of this stimulus .. Could you please see if I did it write and as well my reasoning for eliminating the answer choices ?



"Not surprisingly there are no professors under the age of eighteen " ( am I okay to think that because of the double negatives this is a positive statement)?

Professors --> 18
-18-->not vote

Combined + the rest of the stimulus I get this :
Vote --> Professors --> 18
Brilliant some professors
Brilliant some legal voters
Brilliant some-18

A) nope : opposite direction of our chain
B) nope : we only know about some
C) nope : opposite direction of our chain
D) nope: this is a could be I believe but not a must be ?
E)yes: they can be brilliant people -18 .


Thank you so much
Sherry

[Robert Carroll]

Sherry,

With "no X are Y" statements, although a normal conditional (and its contrapositive) represent the information, the Double-Not Arrow is more compact. Thus:

professor under 18

and

able to vote legally under 18

This also implies things like:

able to vote legally under 18

which might be easier to represent as

able to vote legally 18+

We could similarly say:

professor 18+

Note that the stimulus does not say that everyone who can vote is a professor, nor that all professors can vote. Thus, the chain you have does not correctly represent those relations, and the reversal of the first part still would not represent those relations.

That last sentence involves three different "some" relations:

brilliant person professor

brilliant person legal voter

brilliant person under 18

As far as the answers:

Answer choice (A), note, says that no professors are 18, so that means none are exactly 18. We have no idea. This is not opposite, just unknown, too-specific information.

Answer choice (B) is wrong for exactly the reason you noted. Nothing more to say!

Answer choice (C) is new information.

Answer choice (D) is new information; like you said, it could be true, but is not known.

Answer choice (E) is correct not because there could be, but there must be brilliant people under 18, per the last phrase of the last sentence. Because those people are, by the first two Double-Not Arrows, too young to be professors or legal voters, there are some brilliant people who are neither professors nor legal voters.

Robert Carroll

[MikeJones]

Sherry,

Answer choice (A), note, says that no professors are 18, so that means none are exactly 18. We have no idea. This is not opposite, just unknown, too-specific information.

Answer choice (B) is wrong for exactly the reason you noted. Nothing more to say!

Answer choice (C) is new information.

Answer choice (D) is new information; like you said, it could be true, but is not known.

Answer choice (E) is correct not because there could be, but there must be brilliant people under 18, per the last phrase of the last sentence. Because those people are, by the first two Double-Not Arrows, too young to be professors or legal voters, there are some brilliant people who are neither professors nor legal voters.

Robert Carroll

Hey Robert. Just wanted to inquire about how to interpret the first two conditional statements when combined.

I got:

P-->/U18
U18-->/V

Linked together, we get U18-->/P combined with U18-->/V.
I know this isn't "some P's are not V's" as indicated in answer choice C. And obviously it isn't "some P's are V's."

I just wanted to know if there are any inferences to be made from a combination of those first two statements, since they both lead to negated elements.

[Francis O'Rourke]

Hi Mike,

The first two statements tell us the following:

professor under 18 years old
and
able to vote under 18 years old

I took the contrapositive of the second statement to make the relationship between these two statements clearer. What these two statements tell us is that there are at least two ways to guarantee that someone is not under the age of 18.


We can also take the contrapositive of the first statement to get the following:

under 18 years old professor
and
under 18 years old able to vote

what this tells us is that there are at least two things that you know about someone if you know that they are under the age of 18: they are not a professor and they cannot vote.

Neither of these pairs of statements can be combined to allow for additional inferences. There is no way to know if all professors vote, or if everyone who can't vote is not a professor. Making either of these inferences would require making a Mistaken Negation or a Mistaken Reversal of one of the two conditional statements. This is a relatively common mistake that speakers make in Flaw in the Reasoning questions that involve conditional relationships.


Lacking other facts, there is no inference you can make about B and C if you are given
A B
and
A C

Similarly, there is no inference you can make about X and Y if you are given
X Z
Y Z

Let me know if this answers your question.

[Zach-Fox]

So why not B? I'm assuming I'm over thinking this, but if all brilliant people are either professors, under 18, or 18 or older (legal voter), doesn't the ages create a binary. You're either 18 and up or not?

[KelseyWoods]

Hi Zach!

Careful here--nothing in the stimulus tells us that all people ages 18 and over are legal voters. So based on the statements in the stimulus, there's no reason we couldn't have a brilliant person who is not a professor, is over 18, and is not a legal voter (maybe they are not registered, maybe they are not a citizen, maybe they are a convicted felon, etc.).

Hope this helps!

Best,
Kelsey