#19 - None of the students taking literature are taking

[Txflier]

I'm missing something here.

None of the students taking literature are taking physics, but several of the students taking physics are taking art. In addition, non of the students taking rhetoric are taking physics.

L --> not P
P --> A
R--> not P

answer is A)
A --> not L

[Nikki Siclunov]

You misunderstood the formal logic statement "several of the students taking physics are taking art" to be a conditional statement of the form "P --> A". Just because some students taking physics are taking art does not mean that ALL students taking physics are taking art.

The correct diagram is as follows:

L <--|--> P some A

R <--|--> P some A

If some students taking physics are taking art, it follows that some students taking art are taking physics (a "some" statement can be read backward and forward). However, since no students taking physics are taking rhetoric or literature, we can infer that (1) some students taking art are NOT taking rhetoric; and (2) some students taking art are NOT taking literature.

This is a Formal Logic question - you can find a detailed description of our methodology for attacking such questions on the Student Center under Lesson 8 Homework Supplements.

[Txflier]

Thanks

[stsai]

Q19. "None of the students taking literature..."
I think this is one of those rare formal logic questions, and I used abstraction in diagraming (Lit-A; Physics-B; Art-C; Rhetoric-D) :
No A is B
Some B's are C
No D is B

I was able to eliminate (B)-No A is C; (C)-Some D's are Not A; (D)-No D is A, but I was not sure about (A)-Some C's are Not A, and (E)-A and C.
Is my diagraming flawed at some point?

Thanks so much!

[Nikki Siclunov]

Here's the diagram for this question:

LIT <--/--> PHY some ART

RHET <--/--> PHY some ART

Inferences:

ART some NO LIT

ART some NO RHET

Since a "some" statement can be read backwards, we know that some Art students take Physics. However, no Physics students take Rhetoric or Literature. Therefore, some Art students don't take Literature (answer choice A). We can also conclude that some Art students don't take Rhetoric. However, the fact that there are students taking art but not literature does not mean that there are students taking both art and literature. The inference of the type "ART some LIT" is not available to us given the information provided.

[cmeggs]

Hello, I'm really struggling with this question- "None of the students taking literature are taking physics, but several of the students taking physics are taking art. In addition, none of the students taking rhetoric are taking physics" And then it asks you which answer choice follows logically from that. I guessed D, but the answer is A (There are students who are taking art but not literature). But no matter how much I study it I can't figure out how to arrive at that answer, I'm not even sure how to attack it... why would that answer choice follow above any of the others?

Thanks,

Caitlin

[Rachael Wilkenfeld]

This question relies on formal logic--that is, it requires you to understand the relationship between the variables. We can almost think of the information as rules. So let's break it down bit by bit.

1) None of the students taking literature are taking physics. So if you take literature, you can't take physics (and vice versa). We can represent that as follows L<--I--> P

2) Several of the students taking physics are taking art. While we don't know how many several is, we know it is at least one. So we can say there is at least one person taking both physics and art.

3) None of the students taking rhetoric are taking physics. We can represent that as we did in rule 1. R <---I --> P.

Now let's combine the rules. Let's first look at 1 and 2. If some of the students taking physics are taking art, and no student who takes physics can take literature, then A must be true---there are students who take art but not literature (those art students also taking physics.

We can combine rules 2 and 3 the same way. There are some students who take art, but not rhetoric. This is not an answer choice.

Rules 1 and 3 do not combine. Just because we know you can't take lit and physics, and you can't take rhetoric and physics, we don't know what happens if you try to take lit and rhetoric. Since we don't have information, we cannot make any inference.

Hope that helps!

[cmeggs]

Hello,

Really appreciate it. I had drawn the same thing, but somehow my mind refused to see the connection. Thanks for your help! (I actually think this is a good example of me needing to prephase more, because I just went straight to the answer choices which allowed me to become more confused).

Caitlin

[Basia W]

Good evening,

with regards to diagramming this question, where in our online course books are we taught how to diagrams involving "none" and "several"? Is this an example of formal logic? I was unsure of how to approach this.

Best,

Basia

[Lucas Moreau]

Hello, Basia,

These questions, like most LSAT questions, are much easier if you can break down and rephrase the sentences to be more clear. In this case, let's take the first half of the first sentence.

"None of the students taking literature are taking physics..."

This can be rephrased into a conditional reasoning if-then statement.

"IF a student is taking literature, THEN that student is not taking physics."

The second part:

"...but several of the students taking physics are taking art."

This isn't conditional reasoning, but it stands for this statement:

"NOT NONE of the students are taking both art and physics."

Not none means some, but it can be easier to interpret things in terms of All/Not All, None/Not None, if you have trouble with some and several and those. Last part:

"None of the students taking rhetoric are taking physics."

If/then again:

"IF a student is taking rhetoric, THEN that student is not taking physics."

Summed up:

IF a student is taking literature, THEN that student is not taking physics.
IF a student is taking rhetoric, THEN that student is not taking physics.
NOT NONE of the students are taking both art and physics.

So this shows us that answer choice A must be true. It must be true that some students are taking both art and physics, and it also must be true that a student taking literature is not taking physics. So there must be at least some students that are taking art but not literature.

Hope that helps,
Lucas Moreau