PrepTest 116

Incorrect. Small countries don't have a permanent seat on the UNSC, and that group is the only one we can connect to an opinion on refugees, so this answer is unsupported. (This answer tries to combine statements 1, 3, and 4, which can't be done.)

Incorrect. This answer relies on an illegal negation of statement #3. The negation of statement #3 with statement #2 allows this inference to be drawn, but with the stimulus we have, this can't be inferred.

Incorrect. This answer relies on combining statements #3 and #5, but as we noted in our anticipation, that's not a valid inference. The sufficient condition of the conditional must be shared with the some statement for an inference to be drawn.

Incorrect. This answer relies on an inference from combining statements #1 and #4, but any inference derived from that is about countries that aren't small, so we can eliminate this answer.

Correct. Argument or Facts:
Facts

Question Type:
Must Be True

Stimulus Summary:
(1) Small country → not Permanent seat on UNSC
(2) In southern hemisphere → not Permanent seat on UNSC
(3) Permanent seat on UNSC → Favors more international peacekeeping
(4) Permanent seat on UNSC → Favors greater role for UN in resolving regional disputes
(5) Favors more international peacekeeping—some—Against more UN spending on refugees

Answer Anticipation:
We're going to start by working through the diagramming. This is a Must Be True question with a mix of conditionals and quantified statements, so it's important to get that right to make proper inferences!

We split the first sentence up, which can seem odd—doesn't it have an AND in the sufficient condition, and can't we split sufficient conditions only when they're an OR? The second half of that statement is correct—to split a sufficient condition, we need it to be an OR statement. However, the opening sentence doesn't create a sufficient condition with an AND in it. Rather, it establishes two separate sufficient conditions by splitting the countries up into two groups—it's not any small country in the southern hemisphere, but rather any small country, and also any country in the southern hemisphere. The repetition of the noun here—country"—shows that it's establishing two separate conditional relationships instead of referring to a country that meets two criteria.

Statements 3 and 4 have an AND in the necessary condition, which we can split as a general rule.

Why did we split these? It's a lot easier to work with these simplified conditionals—especially when they're very wordy and hard enough to understand to begin with!

The last statement is a some statement without any tricky language in it.

With that laid out, let's take a look at the statements. #3 and #5 share a term without doing any other work, so there's no need to take the contrapositive of #3. And we can get statements #1 and #2 to share a term with both #3 and #4 if we take the contrapositives of them, so let's do that (and write in the rest just to have them all together):
(1) Permanent seat on UNSC → not Small country
(2) Permanent seat on UNSC → not In southern hemisphere
(3) Permanent seat on UNSC → Favors more international peacekeeping
(4) Permanent seat on UNSC → Favors greater role for UN in resolving regional disputes
(4) Favors more international peacekeeping—some—Against more UN spending on refugees

With that done, we can see that we can combine each of statements #1, #2, #3, and #4 with each other*. It seems as if we should be able to combine statements #3 and #5, but we can't—the shared term between a conditional and a some statements must be in the sufficient condition of the conditional for a valid inference to be drawn!

Even so, that's too many inferences up front, so we should figure out how strong a correct answer can be, and then head down and prioritize answers at that strength, seeing if we can find a combination of statements that justify it. And any combination that can be derived from the stimulus will be a some statement, so that's what we're looking for.

(*Note that two conditionals that share a sufficient condition can be validly combined, just not in a chain. The inference connects the necessary conditions with a some. For instance, if all lawyers are smart and all lawyers are rich, then there are some smart people who are rich—lawyers.)

Answer Explanation:
This answer is a valid inference derived by combining statements #2 and #4. Members with a permanent seat on the UNSC are both not in the southern hemisphere and are in favor of a larger role for the UN in regional disputes, so some countries have both of these characteristics.

Key Takeaway:
Normally, inferences derived from conditionals either chain multiple conditionals together or apply the conditional to a specific case that meets the sufficient condition. However, it's also possible to draw an inference from two conditionals that share the same sufficient condition—it's a some statement that relates the two necessary conditions (since they overlap in the shared sufficient condition).