#25 - Most of the members of the Bargaining Unit Number 17

[kenlars5]

This is how I got D:
BUN17 CP HSB

I see people talking about two mosts to come up with D, what am I missing?

Thanks!

Hi! I’m not an expert by any means but feel I can address your question or perhaps lead you back to the formal logic chapter in the textbook for clarification. As for your question, you have to be careful about what you are connecting some/most statements too... X Y cannot connect with a most statement or another some statement. There is one specific instance with most statements that is worth remembering which is when two most lead away from a common variable. Ex. X <—(most) Y Z from which we can infer that X Z. This is what people are talking about in this thread about 2 most statements.

In this argument this premises states
P: BUN17 CP

It then goes to conclude from this that
C: HB CP

There are two ways that we can essentially draw that conclusion;
1. We can add BUN17 HB. This works because we know that most statements include some (remember that ladder in the textbook where the upper rung include the lower rung) so we confidently say that since BUN17 CP then we are also able to say BUN17 CP. Using this statement we can connect the chain now HB BUN17 CP. From this we can conclude HB CP which is our conclusion.

2. We can use the little exception of two most statements (aforementioned) leading away from a common variable to infer a some statement. For this question since the most statement leads away from the BUN17 that would have to be the common variable, so the most statement that we can add is BUN17 HB. Since Most BUN17 are HB, and most BUN17 are CP then we can infer that at least some HB are CP. To show as a diagram;
HB <—most BUN17 CP = HB CP.
Answer D used this second way.

I hope this was clear. If not I strongly suggest looking back at the formal logic chapter in the Logical Reasoning Bible if you have it available to you.
Good luck!

[theamazingrace]

This is how I got D:
BUN17 CP HSB

I see people talking about two mosts to come up with D, what am I missing?

Thanks!

[Adam Tyson]

Good explanation, kenlars5! You are correct!

Theamazingrace: The goal in this question is to prove the conclusion, which is that "some of the government employees who work in the Hanson Building are computer programmers." We need an answer that connects the evidence to that claim.

Your diagram does not represent the stimulus, and is also not enough to prove the conclusion, so I am not sure where you're going with that. The argument is this:

Premise: BUN17 CP (wherein BUN17 is a group of government employees)

Conclusion: GE in HB CP

We can prove this conclusion by adding another "most" statement about the same group of people, BUN17. Two "most" statements about the same group will require that the two statement overlap. For example:

If most of my children are boys, and if most of my children live in Virginia, then I must have at least one boy that lives in Virginia. Mathematically it is absolutely required, no matter how many children I have.

If most cities are polluted, and if most cities are overcrowded, there has to be at least one overcrowded city that is polluted. Again, no matter how many cities there are, these two "most" conditions about them have to overlap.

Thus, to prove that there are some CP in HB, it would suffice to show that most BUN17 are in HB, That way, we get most BUN17 are CP and most BUN17 are in HB, so there must be some (at least one) CP in HB. No matter how many people are in that Business Unit, the two "most" conditions have to overlap.

As to your statement, it won't prove any connection between BUN17 and HB. Here's another example to show you why:

Most of my pets are cats, and some cats are feral.

Do I have to have some feral pets? Not at all! Those two concepts - "pet" and "feral" - are opposites, so that wouldn't even make sense!

Or try this one:

Most of my students are taking the LSAT this year, and some people taking the LSAT this year are named Zeke.

Do I have to have a student named Zeke? Nope! I might, or I might not, but this chain does nothing to prove that I have even one student by that name.

Let us know if you're still confused about the rules about "most" statements!

[paytenpar2014]

Would someone please explain why the correct answer is not C?

Thanks!

[Poonam Agrawal]

Hi Payten!

Adam's post above does a great job of explaining the formal logic in this question. Distinguishing between answer choice (C) and answer choice (D) can be made even more clear through a numerical example - consider the following situation:

There are three groups of people we are tracking -

1. Bargaining Unit Number 17 (we will call them BUN 17 for short)
2. Computer programmers
3. People who work in the Hanson Building

Let's say that there are 100 people total in BUN 17, 51 of them are computer programmers (most = greater than 50%), and 80 people that work in the Hanson Building. We are trying to say, with certainty, that some (greater than 0%) of the people in the Hanson Building are computer programmers.

If we test out answer choice (C), are we able to make the previous statement with certainty? The answer is no. Even if most employees in the Hanson Building (let's say 41 of them) are a part of BUN 17, all of those 41 people could be part of the 49 non-computer programmers group. In that case, none of them would be computer programmers.

If we test out answer choice (D), our answer changes to yes. If most of the members of BUN 17 work in Hanson (let's say 51 of them), it is impossible for there to be all non-computer programmers in Hanson because there are only 49 non-computer programmers. Therefore, answer choice (D) guarantees that there will be at least one (a.k.a. some) computer programmer in the Hanson Building.

[nivernova]

I have a question about what makes you start diagramming when there are FL questions.

In the first sentence, there is the quantity indicator "most" and it MIGHT but not necessarily imply that the question is FL.

I feel like I will have to finish reading the stimulus(may be the question stem too) in order to determine whether to diagram the relationships in the stimulus.

How can I expect the right timing before reading the whole stimulus which, in turn, makes me re-read for the diagram.

[katehos]

Hi nivernova!

It can be difficult to know exactly when diagramming FL (and even conditional reasoning) will be useful, but usually when I see two references to FL (or conditionals, thereby creating a chain) in a stimulus, I'll make sure to diagram it! Otherwise, I often don't diagram. In this case, we see the word "most" in the first sentence and "some" in the second, so I would be inclined to diagram this, which is further shown to be the ideal method by the answer choices, which all use the word "most".

This is just my personal rule of thumb and everybody is a little bit different! I encourage you to "test" your diagramming to find what works for you! It's a trial and error process, so you'll have to do a decent bit of practice before you find your happy medium -- but you'll find it! Whenever you decide to diagram (or not diagram) a question, ask yourself if the diagram was useful (or if its absence was detrimental)? You can modify your approach based on that to find what works for you!

I hope this helps
Kate