Most train inferences

[HarmonRabb]

Hi, 3 part question, I'm hoping for some guidance on.

Part 1:

I came across a formal logic practice question riddled with somes and mosts on some blog and I was surprised to see they said inferences could be made. I was highly dubious when I saw all the somes and mosts and not a single all.

This is the passage:

There is some debate as to whether great-crested grebes are common in Swansea, but it is known that most grebes live in North Savoy and some grebes live within a mile of a lake. Also, most grebes inhabit boggy areas.

Choose the inference that can be properly made from the premises:

a. Some grebes in Swansea live within a mile of a lake.

b. Some grebes in North Savoy live within a mile of a lake.

c. Some grebes in North Savoy inhabit boggy areas.

The answer provided:

Correct answer: c. This can be a tricky one. The tough part is see that when most members of a group have some characteristic, and most members of the same group also share another characteristic, then there has to be some overlap: at least one grebe is going to have to live in North Savoy and inhabit a boggy area.

Part 2

How would you diagram this? I know arrows don't have to only go horizontally, but my attempted looked nothing like I've come across in PowerScore before, every relationship coming off of "grebes" so nothing chained together.

Part 3:
(Sorry for the long question). I know that only time you can make an inference from two most relationships is A<---m---B---m--->C, but can you give an example of LSAT level text that would yield this relationship? I'm having trouble picturing it past a super simple example.

Thank you very much

[Dana D]

Hye HarmonRabb,

This question actually is an example of the A<---m---B---m--->C relationship you described. Remember that on the LSAT, "most" means 51% or more. So, in this case, more than half of the grebes live in North Savoy, and more than half live in boggy areas. That means that at least one ("some") live both in NS and in a bog. There is no way to account for more than half the population in both conditional statements without having some overlap.

If there are 100 grebes and most live in North Savoy, that means at least 51/100 live in NS. Additionally, we are told most live in a boggy area - again this means at least 51/100 live in a boggy area. There must be at least one grebe that both lives in NS And in a bog, because at least 51/100 of the grebes we are talking about fit into both categories. Does that make sense?

[HarmonRabb]

That's much more clear now, thanks very much!

[HarmonRabb]

Followup question:

I'm not sure I have it nailed down what type of sentence structures yields:

A<----m-----B----m---->C

vs

A----m---->B----m---->C

Is this correct?

Statement A

Most serious students are happy students. Most serious students go to grad school.

happy-students <----m---- serious-students ----m----> grad-school

Statement B

Most high schools have a pool. Most pools have diving boards.

high-school ----m----> pool ----m----> diving-board?

Assuming the way I modelled statement B is correct, is it so because the "mosts" are taking about different things i.e. most high schools and most pools?

[Jeff Wren]

Hi Harmon,

I'm not entirely clear what you are asking, but I'll try to answer as best I can.

First, your diagrams look correct.

In your diagram for statement A, because "serious students" is the shared term and the two" most" statements are about that term (meaning each "most" pertains to the group of "serious students"), it is possible to make an inference here that "some happy students go to grad school" for the same reasons that Dana explained in the previous post.

In your diagram for statement B, because the two "most" statements are about different terms/groups, no inference can be made about high-schools and diving boards.

It may be helpful to use some numbers as an example.

Imagine there are 100 high schools. More than half (i.e. most) have pools.

Let's say 51 of the 100 high schools have pools.

Then we are told that:

More than half (i.e. most) of all pools have diving boards.

However, at this point, for all we know, all 51 of the high schools that have pools may be in the minority of pools that do not have diving boards. In other words, not only do we not know that "Most high schools have diving boards" we don't even know if "Some high schools have diving boards."

[HarmonRabb]

Thanks for clarifying that for me!

[HarmonRabb]

Thanks. This really helped. I posted a followup question to that thread.