Q19 - None of the students talking

[mshinners]

Question Type:
Inference (Must be True)

Stimulus Breakdown:
L → -P
P -some- A
R → -P

Answer Anticipation:
Ugh, quantifiers…

Since we can't work with the "some" statement to get overlap between it and the P terms in the first and third conditionals, we should contrapose those two to get:
1) P → -L
2) P -some- A
3) P → -R

There are rules for combining quantified statements which, if you don't know, you should review! Download our flashcards.
1+2) -L -some- A
1+3) -L -some- -R (this probably won't be the answer)
2+3) A -some- -R

Correct Answer:
(A)

Answer Choice Analysis:
(A) Bingo. This is the combination of statements 1 and 2. It's the reverse of what I wrote out above, but "some" statements are reversible.

(B) Degree. This is too strong. I can't get a "none/all" answer in these unless I can chain two "none/all" statements together. In this question, the two all statements share a sufficient condition, so they don't chain.

(C) Unsupported. We know there are some students who are not taking literature and are also not taking rhetoric, but that doesn't mean there are some who are taking rhetoric. This is the difference between how we use "some" in the real world (to set a min and a max - "There are a few, but not a lot") and how the LSAT uses it (to set a min - "There are guaranteed to be a few, but it might be all of them.").

(D) Degree. This is too strong. I can't get a "none/all" answer in these unless I can chain two "none/all" statements together. In this question, the two all statements share a sufficient condition, so they don't chain.

(E) Unsupported. From combining statements 1 and 2, we can say that some art students aren't taking literature, but this doesn't guarantee that some are taking it. See the discussion for (C) for a longer discussion on this.

Takeaway/Pattern: Learn your quantifiers! Download the flashcards. It's usually good for a question or two on the exam.

#officialexplanation

[Raiderblue17]

I got the answer right, but i just want to see why the other answers are wrong.

I picked A b/c I knew that it could connect back to the others.

(Riding the "some train" according to the LGB)

[timmydoeslsat]

I diagrammed it like this:


A some P ---> ~L and ~R

Interpretations of this diagram:

We know that there are some students that take A and P.

Since we know that there are at least some A with P, and that when you have a P, you DO NOT HAVE L and you DO NOT have R.

Thus, we know we have some A with ~L and ~R.

Answer choice A fits.

B) Can be seen as this: L ---> ~A

We cannot infer this. We know that if we have L, we do not have P. If we do not have P, we know that we would be without some of the make up A, but we do not know that ALL of them would be gone.

C) Can be seen as this: R some ~L

We cannot infer anything about those two relating to one another.

D) Can be seen as this: R ---> ~L

Same issue. We cannot infer anything about those two variables relating to one another.

E) Can be seen as this: A some L

We do not know this as a fact. We know that there are "A some ~L" but we do not know that we have "A some L."

[cdjmarmon]

Should it be

Some P-->A since it says several of the students taking physics are taking art.

Overall I cannot answer these questions and would appreciate some help. Especially since I take the LSAT in about a week.

[timmydoeslsat]

Should it be

Some P-->A since it says several of the students taking physics are taking art.

Overall I cannot answer these questions and would appreciate some help. Especially since I take the LSAT in about a week.

I would drop the arrows with the some statements.

When you are telling me that some P are taking A, you can diagram it lik:

P some A

This is a some statement and these statements are always reversible. Telling me that P some A is the exact same thing as A some P.

Now, the other information in the stimulus tells us that:

L ---> ~P
R --->~P

We can flip this to make easy inferences from it:

P ---> ~L and ~R

We also know that A some P.

A some P ---> ~L and ~R

This is called a syllogism. We have a major premise of P always leading to not L and not R. We also have a minor premise of a some statement. We can now make an inference about the variable of A.

We know that some A will also be ~L and ~R.

We know that some A is a P. And we know that every single P is a ~L and ~R. This leads to this inference of A sometimes being ~L and ~R.

[cdjmarmon]

Thank you you explanation makes sense. However, I am still confused on a few things even after reviewing them in the Manhattan book.

So "Some" statements can go both ways as in: P<some>A - some A are P and some P are A?

What if it said P some ~A would that mean ~A some P?

I also know All L -> ~P and All R -> ~P as well as the contrapositive All P -> ~L and ~R.

But what if it was All L -> P and All R -> P? Would that mean
All ~P -> ~L and ~R?

I seem to remember someone saying "all" statements are reversible but they only equal "some" in reverse not "all". Im all over the place here lol.

--------------------------------------------------------------------------
UPDATE: We can reverse all, some, and most statements into some statements as long as there is no negative right?

As in All A are B, Most A are B, and Some A are B = Some B are A for all three counts?

However, All A are not B, Most A are not B, and Some A are not B can only be reveresed into Some ~B are A and I can't take the contrapositive of the Most or Some statements, only the All statement?

Can anyone just post the concrete rules for All, Most, and Some in regards when we have A->B, A->~B,~A->~B?

[timmydoeslsat]

So "Some" statements can go both ways as in: P<some>A - some A are P and some P are A?

Absolutely they do. If I tell you that some students wear green shirts. Then some people who wear green shirts are students.

What if it said P some ~A would that mean ~A some P?

Absolutely.

I also know All L -> ~P and All R -> ~P as well as the contrapositive All P -> ~L and ~R.

But what if it was All L -> P and All R -> P? Would that mean
All ~P -> ~L and ~R?

I will first say that there is no need to say all L ---> ~P

Simply saying L ---> ~P is fine. That implies that all L are in fact ~P. We denote all statements with conditional relationships.

And you are correct on your contrapositive statement. If we know that L ---> P and R ---P.....then not having P will lead us to not having L and to not having P.

I seem to remember someone saying "all" statements are reversible but they only equal "some" in reverse not "all". Im all over the place here lol.

That is also true. If I know that every A is a B, I know that A ---> B

I also know that if some B's in the world are A's. We have to know that A's do exist in the world.

When you do know that you do have the sufficient condition being met in an A ---> B relationship, you do know that some B's are A's, which is to say that some A's are B's (some statements are reversible).

UPDATE: We can reverse all, some, and most statements into some statements as long as there is no negative right?

The negative is not a factor in terms of accompanying a variable in logic. For instance:

If I know that....~X ---> Y

And I know that I have a case of ~X, I know that I have a case of Y some ~X, which is to say that I have ~X some Y, as you can reverse some statements.

As in All A are B, Most A are B, and Some A are B = Some B are A for all three counts?

Yes. The only concern is in the first statement of All A are B. We have to know that at least one A exists in the world. We can then derive the inference of A some B, which is just like B some A.

However, All A are not B, Most A are not B, and Some A are not B can only be reveresed into Some ~B are A and I can't take the contrapositive of the Most or Some statements, only the All statement?

That is correct that you cannot take contrapositives of quantifying statements such as some and most. The contrapositive is simply the idea of showing that a necessary component not being met will ensure the absence of the sufficient variable. This idea of sufficient and necessary is not being addressed by quantifying statements. We do not know what is sufficient and what is necessary with these kinds of statements.

Can anyone just post the concrete rules for All, Most, and Some in regards when we have A->B, A->~B,~A->~B?

All of those conditional relationships you have posted work in the same manner. The fact that a certain variable is negative does not impact in the way we make inferences.

Here are my need-to-know ideas for dealing with logical inference question stems:

A some B

Can be reversed as B some A with no problem.

This also does not rule out the possibility of all A's being B's, we simply cannot tell from this statement.

A most B

Can be reversed as B some A. We know that if most A's are B's, we must have some B's be A's in the world. We do not have to worry, like we do in the conditional relationship, about whether or not A exists, as we know that A exists by the very fact that we know something about most A's, which means they necessarily are existing in the world. (Same holds true with the prior paragraph concerning a some statement. We know that A is existing in the world since we know something about some A's.

Conditional relationship of A --->B

If we do know that A exists in the world, we know that we will have some B's that are A's, which we can state as a simple B some A, which can be reversed as A some B.

This conditional relationship is the same regardless of the positive/negative status of the variables.

[giladedelman]

Good explanation!

[aerialstrong]

A new approach which is , i think, more exam-oriented, though all of ur explaination has been clear:

The type of " some" "more" question usually appears towards the end of the logic reasoning test. ur strategy of diagramming will eventually solve the problem, but too time consuming.

B, C, D, E are wrong for they all make an assertion about relations that is not asserted in the description as non-exist. while A says, the relation that is not mentioned in the description could possibly exist.

This one for example, the only 3 certain relations described are, L and P, R and P, and P and A, so if the choices make any assertion beyond those 3 relations, whatever they are, are wrong.

[timmydoeslsat]

A new approach which is , i think, more exam-oriented, though all of ur explaination has been clear:

The type of " some" "more" question usually appears towards the end of the logic reasoning test. ur strategy of diagramming will eventually solve the problem, but too time consuming.

B, C, D, E are wrong for they all make an assertion about relations that is not asserted in the description.

This one for example, the only 3 certain relations described are, L and P, R and P, and P and A, so if the choices make any assertion beyond those 3 relations, whatever they are, are wrong.

Too time consuming? It would take a person not even 30 seconds to jot this down:

P ---> ~R and ~L
P some A

So hunt for answer that focuses on the syllogism of A being an ~R or a ~L.

I am not sure what you mean by an answer choice going beyond an assertion of those 3 variables. I do not see an answer choice that does it.

[aerialstrong]

A new approach which is , i think, more exam-oriented, though all of ur explaination has been clear:

The type of " some" "more" question usually appears towards the end of the logic reasoning test. ur strategy of diagramming will eventually solve the problem, but too time consuming.

B, C, D, E are wrong for they all make an assertion about relations that is not asserted in the description.

This one for example, the only 3 certain relations described are, L and P, R and P, and P and A, so if the choices make any assertion beyond those 3 relations, whatever they are, are wrong.

Too time consuming? It would take a person not even 30 seconds to jot this down:

P ---> ~R and ~L
P some A

So hunt for answer that focuses on the syllogism of A being an ~R or a ~L.

I am not sure what you mean by an answer choice going beyond an assertion of those 3 variables. I do not see an answer choice that does it.

I just revised my language of explaination above...sorry, non-native English speaker.

B, C, D, E are wrong for they all make an assertion about relations that is not asserted in the description as non-exist. while A says, the relation that is not mentioned in the description could possibly exist.


It's just another way of thinking...probably will work for those who find diagramming too time consuming like me. So i don't usually do that unless necessary. and in my way, i chose the answer instantly after reading the description.

[timmydoeslsat]

That is wonderful if you can perform that way during a test! To me, that is rather taxing mentally when I can just write down a couple of statements and combine them.

[steves]

I first tried diagramming similar to those above and got this one wrong. It now seems easier to start with circle diagrams for this question.

The circles for P and A intersect--and have some common students. The circles for P and L, and for P and R do not intersect. Since there are some within A that are also within P, we know those students can't be within the L circle since P and L don't intersect.

I had earlier chosen (E), but looking at the circles, we don't know whether the circles for A and L intersect or not.