#17 - No small countries and no countries in the southern

[Nikki Siclunov]

Hi amna.ali467,

Thanks for your question.

The stimulus contains the following conditional/formal logic statements:

Security Council Small country

Security Council Southern semi.

Security Council Increased peacekeeping AND greater UN role

Increased peacekeeping against increased spending

Since we don't know if every country in favor of increased peacekeeping is on the SC (that would be a MR), we cannot determine anything about the countries that are against increased spending on refugees. This eliminates answer choices (A) and (C). We also don't know what must be true about any country NOT on the security council, which eliminates (B) and (D). This leaves us with answer choice (E): some countries that favor a greater UN role (namely, countries on the SC) are not located in the souther hemisphere (given the second statement, above).

If you are a student in one of our Full Length or Live Online courses, you may consult the Formal Logic supplement and virtual module, available on the Online Student Center under Lesson 8.

Thanks!

[ehilliard]

Hi,

I read the other posting referencing this question but I am still confused by it.

The diagram I used was:

If Permanent seat international peacekeeping & greater role regional disputes

If not int'l peacekeeping or not regional disputes not permanent (maybe small country, maybe from southern hemisphere)

I don't follow how E comes about. Reading the stimulus I felt that the only countries we really knew were on the committee were the five permanents so it seemed a stretch to me to infer anything about the smaller countries.

Thanks,
Erin

[Dave Killoran]

Hi Erin,

This is a tough one, and only about 1/3 of test takers answer this one correctly. I can say that a good portion of being able to navigate this question comes from knowing what inferences can be made, and looking for the answer that is by far most likely to result from these relationships. So, let's look at it and see what we can determine.

The first sentence is actually critical, and it's also a bit confusing. If you are a small country, or a country in the southern hemisphere, then you do NOT have a permanent seat on the council. Since that's a positive sufficient condition and a negative necessary condition, I just turn that into a double-arrow:

• Small country
  or Permanent Seat
  Country Southern Hem

When I did this problem, I actually used two double-not arrows (and wrote this in reverse order), but the graphics of this forum don't allow me to show that easily. If you put a term between Small Country and Country Southern Hem it would be an "or" as shown above because if you get either one, you don't have a permanent seat. If that doesn't make sense, ask me about it and I'll break it down further

Then, as you note, countries with a Permanent Seat are in favor of increased efforts and a greater role. I reduced that second term to simply "In Favor" but it doesn't really matter; yours works equally well:

• Small Country
  or Permanent Seat In Favor
  Country Southern Hem

At this point, we have enough for (E). Starting at In Favor, we can ride back across the arrow using "some," and then travel to "Country Southern Hem," tossing a negative onto that from the double-not arrow. So, effectively, my inference is that "In Favor some are not Country Southern Hem." That's what (E) says, and that's the answer.

The last sentence of the stimulus is notable because it tosses a new "some" relationship into the mix, and one that would attach to part of the "In Favor" statement. However, I automatically threw that out an didn't even analyze it. Why? Because the basic form of it can't produce an inference. Take a look at the following relationship:

• A B C

Can I draw an inference there? No, you can't because the arrow is pointing the "wrong" way in order to work with "some." The stimulus attempts to add a sort of ":some: C" portion to In Favor, and that can't work so I just went right past it. At that point I knew that "In Favor some are not Country Southern Hem" (or "In Favor some are not Small Country") had to be the answer, so I went looking for that.

That's a really quick, causal explanation, but I hope it helps. Please let me know. Thanks!

[ehilliard]

That was extremely helpful, thank you so much for outlining that in detail. The trap I fell into was keeping the diagrams separate. I didn't see that linking piece which allows for the inference in E.

Can you explain what you meant by not being able to make an inference out of the last statement? Not being able to go backwards on that arrow?

[Jon Denning]

Let me jump in here and see if I can help clarify things. That last statement was this:

A B C

I'll try to explain the reasoning here with a numerical-style approach. The reason you can't make any inferences about the relationship between A and C (you can't go backwards, as Dave suggests) is because A is contained, in a sense, within B, but we don't know how much of B is not A. Since the overlap of B and C can exist outside the part of B that is A, then we can't know with certainty that A and C "touch," or overlap.

Imagine that A has 10 members, and all 10 As are in group B, which has 100 members. Some of the 100 members of B are also in C. It's possible that the members of B who are also in C are part of the original A (there are 10 candidates after all), but it's far from guaranteed: 90 members of B are NOT from A, and any of those 90 could be the "some C" overlap. So we can't know anything about A and C's connection; some A might be in C, but it's possible no As are in C...thus we have no inference.

Were the arrow pointing from B to A, where we could go from the some C to B and continue moving in that direction to A, then we would have the inference A C, but in this case the arrow is pointing the wrong way and we can't know anything.

[PVequalsnRT]

So, in this question, if the scenario had PS > For international peacekeeping efforts (but not also a greater role in moderating); could we draw the inference PS some> against increased spending? Is this why we cannot make the or inference with the increased spending and moderating disputes?

[Luke Haqq]

Hi PVequalsnRT!

In understanding why we wouldn't be able to draw the inference "PS some> against increased spending," let's break down the conditional reasoning (I use a ~ and parentheses to represent "not"):

No small countries and no countries in the southern hemisphere have permanent seats on the United Nations Security Council.

- small country ~(permanent seat)
- southern hemisphere ~(permanent seat)

Each of the five countries with a permanent seat on the Security Council is in favor of increased international peacekeeping efforts and a greater role for the United Nations in moderating regional disputes.

- permanent seat favor of increased international peacekeeping efforts + greater role moderating disputes

However, some countries that are in favor of increased international peacekeeping efforts are firmly against increased spending on refugees by the United Nations.

- favor of increased international peacekeeping efforts ~(increased spending on refugees)

With these diagrams, we can indeed build a chain:

- permanent seat favor of increased international peacekeeping efforts ~(increased spending on refugees)

However, this construction (A B C) doesn't permit the inference A C. Rather, for that we would have needed something in the form of A B C.

[nusheenaparvizi]

I had a small question that threw me off against AC (E). The word "some." In the stimulus, it states that NO small countries and NO countries located in the southern hemisphere have permanent seats on the UNSC. I eliminated (E) because it said "some" countries and thought that the countries that favor increased peacekeeping & moderating regional disputes were all members of the UNSC, thus, none of them are small countries or located in the southern hemisphere. How could "some" countries that are in favor of moderating regional disputes be the right answer? Shouldn't it be ALL countries?

Thank you!

[KelseyWoods]

Hi nusheenaparvizi!

Careful here--we know that all members of the Security Council are in favor of a greater role for the UN in moderating political disputes. But that doesn't mean that Security Council members are the only countries in favor of a greater role for the UN in moderating political disputes. That would be a Mistaken Reversal of the statement. We don't know that ALL of the countries in favor of a greater role for the UN in moderating political disputes are on the Security Council. We only know that ALL of the countries on the Security Council are in favor of a greater role for the UN in moderating political disputes. Which means that some of the countries in favor of a greater role for the UN in moderating political disputes are on the Security Council which means that some of those countries are not in the Southern Hemisphere.

But, incidentally, let's say in another Must Be True question you have a scenario where you can make an inference including "All" and they give you an answer choice with "Some." Let's say the stimulus says "All cats are fluffy" and there's an answer choice that says "Some cats are fluffy." If it's true that ALL cats are fluffy, isn't it also true that SOME cats are fluffy? If I have ALL of something, then I also have SOME of something. But it doesn't work the other way around--if I have SOME of something, I don't necessarily have ALL of something (though it's possible I do!). And even if I can prove more than what the answer choice gives me, it doesn't change the truth of the answer choice.

Again, we're not applying that exact principle here because our stimulus in this question only supports the "some" in answer choice (E) and not "all." But it's worth noting for future questions.

Hope this helps!

Best,
Kelsey

[MayaPapaya]

Hi,

I am wondering why the first sentence is diagrammed as no small countries OR no countries in southern hemisphere instead of AND. Even though it says "and," do we use OR because we can assume they are separate entities? I'm afraid of assuming things on this test

Also, how do we draw the conclusion in the answer choice from the following final conditional we arrive at:

~SC + ~SH <--some--> IP + MD

From this how can we just say MD <--some--> ~SH? How can we just pull those two terms out if they are in AND statements? I thought we could only do that if it is an OR statement.