Formal Logic Problem Set #3

[Forwardever]

Dear David,

I am a bit lost on this question. I found it on Logical Reasoning Bible:

Most serious students are happy students...

Now, I was told the answer is B. I am still at a loss why it is B. I thought it was C. Can you elaborate why it is B please? Many thanks to you.

[Charlie Melman]

Hi Forward,

The statements in the stimulus can be diagrammed as follows:

S H

S G

G O

We can use numbers to prove that answer choice (B) is correct. Say there are 10 serious students. That means at least 6 are happy. If most serious students go to graduate school, then it must be true that at least one happy student goes to graduate school. (You can draw this out on paper to see why this is true.) Since all graduate school students are overworked, then there must be at least one happy student who is overworked. This is the same as saying that "some" happy students are overworked.

Answer choice (C) is equivalent to saying O S. it's possible that there are some overworked students who aren't serious. We can infer that some overworked students are serious, but the stimulus just does not give us enough information for us to infer that they all are.

Hope this clears things up.

[Forwardever]

Dear Charlie,

Thank you so much. I appreciate your kind help.

Forward

[Dave Killoran]

Hey Forward,

A quick note on that question since you asked about it's appearance in Chapter 2: it's just a sample question to display a tough problem that will get easier after you read the book. Once you read and absorb Chapter 13, that problem will be easy.

Thanks!

[Dave Killoran]

In response to a PM I received, I wrote the following:

Yes, I feared that the explanation above would be a bit challenging because Charlie is rightly using symbols and ideas from much later in the book. As I state in the text of the book, this is a sample problem and not one meant to be worried about at this point. The fact that you are struggling with it is a perfect example of why I placed it there—it's tough to do now, but after you read the book that problem will be easy. It's like a calculus problem they show you at the start of a math book. To explain it, you need calculus, and that's what Charlie did

So, that said, there's very little value here in worrying about this problem because what I'll say about it is not exactly how you'll solve this later, if that makes sense.

With (C), it's way too strong. you know that most Serious Students are Grad students, and all grad students are Overworked, but that "most" in the chain kills any hope of an "all" statement as the conclusion. Plus, the terms are reversed (which will be covered in Ch6), so that's a second problem there.

With (B), this is tricky, but the two "mosts" emanating from Serious Students overlap, creating a "some" inference that is properly stated in (B). Let's use an analogy:

• Most of the students at Harvard are Rich, and most of the students at Harvard are Famous. Well, let's imagine there are 5 students at Harvard. If most are Rich, that means that at least 3 are rich. If most are Famous, that means at least 3 are Famous. Well, those groups of 3 overlap at some point, which means that at least one student is both Rich and Famous.

In our example above:

• Students at Harvard = Serious Students
  Rich = Happy Students
  Famous = Grad School

So, in other words, this is ultimately a situation where the groups involved overlap, which proves that (B) must occur.

Ok, all that aside, don't worry about this again for a while. Chapter 6 is going to really open your eyes to some cool ideas, and then Ch13 will further expand ideas into a whole system where concepts like the ones above make perfect sense. You will be able to crush a problem like the above in 45-50 seconds.

Please let me know if that helps. Thanks!

[esther913]

Hi,
I have a question regarding answer choice (D) and the some inference.
Can I "logically negate" a some relationship?

I diagrammed (D) as Not H GS and was wondering if I could arrive to (D) from the inference H GS.

Clarification would be greatly appreciated!
Thank you.

[Dave Killoran]

Hi Esther,

Thanks for the question, and sorry for the delay—I've been out of town!

You cannot make this transition Since some can include all, you cannot say that some implies some are not.

The cool thing though is that the LSAT gives this away since (D) is an incorrect answer. It's one reason why we always say to study the incorrect answers as well, since there is plenty to learn there

Thanks!

[esther913]

Thank you for the clear explanation!
The advice at the end was very helpful too, thank you