Lesson 8, Page 26, About Formal Logic

[SherryZ]

Hi there,

I read Lesson 8 Formal Logic. There is a question that I don't understand. Thanks for helping me in advance!

On page 26 of the Lesson 8 Supplemental Material of Formal Logic, it says B A and B C, then we can conclude A C. WHY???

Based on the previous page, B A, we can make inference that B A. Similarly, B C, we can infer that B C. Therefore, the relation becomes A B C.
But when there are two consecutive SOME/MOST, or ONE SOME + ONE MOST, a statement does NOT yield additive inference.

I AM SO CONFUSED AND DIZZY PLEASE HELP Thanks a lot!!


Sincerely,
Sherry

[Dave Killoran]

Hi Sherry,

Note for other students: the reference here is to page 26 of the Formal Logic Supplement in the Lesson 8 area of the Online Student Center.

The situation you reference is a rare one, and is one of the only times that two Mosts yield an inference when combined (I'll reference the other time below, but you're not likely to ever see it on the LSAT because it it involves specific numbers). In both cases however, it's not the typical Some/Most relationships that force these inferences--it's about the numbers involved in the groups. The text on page 26 references these situations, but please let me take a moment to explain in more detail.

In the scenario you ask about, the key is that both Mosts originate from the same source:


B
A
C


Because "most" means more than half, if more than half of the As are Bs, and more than half of the As are Cs, then at least one B is a C. Let's look at this numerically to really clarify the point:

• Imagine that we have a group of 7 automobiles (A), and that most of them are Blue (B), and also that most of the Automobiles have Corinthian leather interiors (C).
  
  If most of the automobiles are Blue, then at least 4 are Blue. And if most of the automobiles have Corinthian leather, then at least 4 have Corinthian leather. So, if that is the case, then you have to have some overlap between the Blue cars and the Corinthian leather cars (because taking 4 out of 7 only leaves you with 3, yet the other group has 4 or more). So, there is always an overlap, and at least one blue car has Corinthian leather. And thus, some Bs are Cs.

So, that is one scenario where two Mosts yield an inference, and it is the only scenario that LSAC tests with any regularity.

However, there is another possible scenario where you could have two Mosts combine to yield a Some inference. This scenario requires so much additional information that it is unlikely to ever be tested by LSAC. The scenario appears as follows:

• 1. You have a classic A B C scenario
  
  AND
  
  2. You know the relative numbers of three groups, and they are descending.
  
  For example, if there are 7 As, 5 Bs, and 4 Cs, it turns out that some of the As must be Cs. So, they could at some point test this idea, but to do so would require providing a lot of relatively specific numerical information.

Please let me know if that helps. Thanks!

[SherryZ]

Dear Dave,

First of all, thank you very much for answering my question!

You mentioned that "A B and A C" is about the numbers involved in the groups. Do you mean that unless the stimulus presents specific numbers, we CANNOT infer that B C?

Thanks again!

---Sherry

[Dave Killoran]

Hi Sherry,

No, although it relates to numbers, you don't need them to make the inference--it is always there. I'd recommend taking a second look at my explanation to see how that point works; I'm worried the underlying relationship and how it works may not be entirely clear to you just yet

I used numbers in that first discussion example in order to make it clearer. But, it was only in the second inference discussion that I noted that having numerical information was required.

Thanks!

[SherryZ]

Dear Dave,

Thank you for responding my question so quickly!

If A B and A C can work, why does its inference B A C cannot work??

Thank you again!

---Sherry

[Dave Killoran]

Hi Sherry,

Let me turn that around on you Why do you think it doesn't work?

Thanks!

[SherryZ]

Hi Dave,

I think B A C does not work because, first, the Formal Logic said so ("two some cannot generate inference..."); Second, because numerically, it might not have overlap. Could you tell me what mistake I made?

Thank you!

---Sherry

[Dave Killoran]

Hi Sherry,

You haven't made a mistake so far Can you give me an example numerically of why it doesn't have to produce an inference?

Thanks!

[SherryZ]

Dear Dave,

I come up an example to prove that B A C CANNOT generate inference:

Assume B has 20 in total, A has 20too, so does C.
3 Bs are A, 5 are C. However, we cannot infer that B C.

What do you think?

So far I am still so confused that why A B and A C can generate inference, but its inference B A C cannot

---Sherry

[Dave Killoran]

Hi Sherry,

Sure, that example works just fine!

As far as the last part, the reason is the difference in the strength of the terms. "Most" is a much stronger term than "some," and that completely changes what is possible. I still think you may be slightly unclear on why this relationship:


B
A
C


generates a viable inference. Please take a look at that very closely

Please let me know if that helps. Thanks!