#22 - Nursing schools cannot attract a greater number of

[Steve Stein]

Hi,

It seems like you've got the diagram of the stimulus right--so take another look: if the pool doesnt increase, they will either have to lower their standards. or there will be an acute shortage of nurses.
So, maybe they will lower their standards and thus avert a shortage. The author points out that this is not guaranteed--but it still could happen. That's why we cannot reliably conclude that there will soon be an acute shortage of nurses.

I hope that's helpful! Please let me know whether this is clear--thanks!

~Steve

[Jalarcon]

Thank you for your quick reply and yes it was very helpful.

[Jon Denning]

I was asked about this question from a student earlier today, and while my answer largely echoes what's already been posted in this thread, I figured I'd include it anyway

The stimulus tells us that nursing schools can't attract more applicants unless the problems of low wages and high stress are solved. That’s conditional (note the “cannot”) so we can represent it like this:

More applicants Solve problems [I’m abbreviating here rather than mentioning the specific problems, because the problems are never treated individually in this question]

The contrapositive then is:

NOT solve problems NOT more applicants

Keep in mind of course that the “original” and the “contrapositive” are two versions of the same thing, so if you started with what I’ve shown above as the contrapositive that’s totally okay!

Next, we’re told that if schools don't get more applicants they’ll have to either lower entrance standards or face a shortage of nurses. Again, the strong language indicates conditionality:

Lower standards
NOT more applicants or
Shortage

Because there’s a shared term in this new statement and the original contrapositive—NOT more applicants—we can link them:

lower standards
NOT solve problems NOT more applicants or
shortage

Last, we’re told that if either lower standards or a nurse shortage occurs then the high quality of health care cannot be maintained. Another piece to the chain above:

lower standards
NOT solve problems NOT more applicants or NOT high quality healthcare
shortage


So far so good, hopefully. Now we need to prove an answer choice.

Answer choice (C): This is a classic Mistaken Negation. It says: Solve problems High quality healthcare. That’s the exact opposite of what we have above: NOT solve problems NOT high quality healthcare. Remember, when your sufficient condition is gone (in this case when we don’t see “NOT solve problems,” or one of the other sufficients) you know NOTHING. Saying simply “solve problems” means you can’t go anywhere.

Answer choice (E): Pay attention to the “if” in this statement. Whatever “if” modifies starts the chain, so (E) gives us this: [If] NOT solve problems NOT high quality healthcare. That’s exactly what we have above when we follow the arrows from the first term all the way to the last term.


I know this is tricky, and probably frustrating, but fortunately there really are rules that govern it. In the question here knowing that any “if” statements are immediately sufficient (in front of the arrow) allows you to quickly distinguish between otherwise similar-looking answers

[jgray]

I diagrammed the first sentence with two necessary conditions joined by "and." That caused confusion moving forward due to similarity with the other multiple necessary conditions in the second sentence. Any recommended techniques to check ourselves or determine when to list out multiples or group them?

[Kristina Moen]

Hi jgray,

You can still solve this by using your method and writing two necessary conditions for the first sentence. Just remember that "and" switches to "or" when you flip and negate (when you write the contrapositive). If two conditions are necessary for a sufficient condition, then if just ONE of them doesn't occur, the sufficient doesn't occur. Here, the answer choice included both necessary conditions, which is why it might be easier to explain it as one condition. However, the answer choice could have included just one of the necessary conditions (solving problem of low wages, solving problem of high-stress working condition) and it would still be correct. So it's not an issue that you wrote it as two necessary conditions. It sounds like you went astray when you tried to link them together. If it's helpful, review Chain Relationships in Conditional Reasoning. The stimulus gave us this structure:
A B & C
Not A DorE
DorE F

We can link this as Not B & C Not A DorE F. The correct answer choice said Not B & C F.

[rohall]

Hi Ellen,

That one presents a series of conditional statements about the state of nursing:

Nursing schools cant get more applicants unless the solve wage and stress problems:

More applicants solve wage and stress problems

Contrapositive:

NOT solve problems NOT more applicants

If they don't get more applicants, that means either lower standards or a shortage:

lower standards
NOT more applicants or
shortage

Linking this with the contrapositive above, we get the following:

lower standards
NOT solve problems NOT more applicants or
shortage

Answer choice B:
NOT more applicants lower standards

We cannot confirm that schools will lower their standards because of the "or" in the stimulus diagram--there might be a shortage of nurses instead.

Answer choice D:
NOT solve problems shortage

We cannot confirm that this would lead to a shortage, for basically the same reason--the "or." The schools might lower their standards instead of having to deal with a shortage.

I hope that's helpful--please let me know whether this is clear--thanks!

~Steve

Hi there, How do we know when to link them? Why did we link before doing the second contrapositive?

[Rachael Wilkenfeld]

Hi Rohall,

The great and powerful thing about conditional reasoning is that you can link statements that have the same term in the sufficient of one statement, and the necessary of the other. The linkages can provide powerful inferences. But the terms have to be the same exactly. You can't link them if one says "Bears dance all night" and another says "Bears do not dance all night." And you can't link them if the same term is in the sufficient of each or the necessary of each. But that's where the contrapositive can come in and help.

So let's look at what we have here:

More applicants Solve problems

Lower standards
NOT more applicants or
Shortage

On first glance, we can't link those two conditionals because 1) the term in common " more applicants" is positive in the first conditional but negative in the second, and 2) it's in the sufficient in both, so we couldn't link them even if they were the same.

Both of these issues can be solved though by taking the contrapositive. And so our first statement becomes
NOT solve problems NOT more applicants

That links easily to our second statement, and we can easily make a chain.

lower standards
NOT solve problems NOT more applicants or
shortage


Hope that helps!

[tdpatel]

Hi PS,

Not sure if this question was already asked,

Would be it be ok if instead of saying, AGN = PNI, I instead said /PI (I am using the / as a symbol for NOT)?

Pardon my typing, I do not know how to add a strike-through on text

So then my diagram becomes /AGN = /PI

Then I can use that to make my full diagram:

PS /AGN=/PI LS or AS /HM

Could this be a correct way of diagramming the problem?

Hopefully this makes sense!

Cheers!

[Dave Killoran]

Hi TD,

In general, substituting whatever symbol you want is just fine, as long as you understand it! So, we might use one representation, and you may use a different one, but as long as it makes sense to you and results in the same inferences, there's no harm.

I'm not totally following you above, but as long as it's consistent with the advice in the prior paragraph, you're good.

Thanks!

[tdpatel]

Hi Dave,

Thanks for your response, I realized that I was saying the same thing, I was just representing it in a different way.

Cheers!

- Taj Patel