Necessary and Sufficient Indicators

[alluv001]

Hello all,

Couple questions,

I've noticed that in some stimuli a premise will have either a sufficient/necessary indicator and the word "and" thus pointing to there being 2 separate sufficient/necessary conditions. However, instead of being diagrammed as shown in lesson 2 with a "+" demonstrating the "and", the explanation for the problem simply joins both conditions into one sufficient or one necessary condition.

For example, #12 on page 2-65. The sentence says "...unless the problems of low wages and high stress working conditions are solved".

Question 1) why is it that in this case it is diagrammed as "PS (Problem Solved), instead of LW (low wages) + HS (High stress)?

Question 2) I'm having trouble understanding question #12 as a whole, can you elaborate?

Question 3) I'm having a hard time identifying sufficient and necessary relationships when the key words (Such as those provided in the lesson) aren't present. For example, words such as "since" and "cannot". I know the key words are not be memorized but rather understood, but I'm having a hard time putting this into effect when it comes to the language presented in some stimuli. Any tips/advice?

As always,

thanks!

[Jon Denning]

Hey alluv,

Thanks for the questions. Let me take them one at a time in multiple replies, since I think all three are worth discussing and each raises valuable points.

For #1, let's talk briefly about diagramming. In this case the diagram chosen is mostly just a choice of convenience, as a lot of diagrammatic abbreviations tend to be. Saying "problems solved" covers the specific problems mentioned (low wages and stressful working conditions), so solving them means they're both fixed, and "problems not solved" means at least one, possibly both, haven't been corrected.

What I always encourage students to consider when they diagram is that (1) they're accurate. Diagrams are nothing but trouble if you've reversed something, or shown "and" as "or," or made some other mistake. (2) they're comprehensible. That is, whatever abbreviations you choose to use are not only appropriate for the text, but you can understand what they refer to when looking at your diagram. (3) they're efficient. Diagrams are meant to be quick sketches to more visually represent bulkier sections of text (pictures for language, roughly), so if you get too text heavy you start to really undermine the whole purpose of the diagram itself.

With those in mind, taking another look at this question you can see that the diagram we chose fits all three!

I hope that helps, and your next two question explanations are coming in just a minute!

[Jon Denning]

Your second question is about #12 in general, so let me see if I can break this one down a bit.

The first sentence tells us, and I'm going to reword it a little bit to simplify (hopefully your diagram represents what I'm about to say), that if nursing schools attract more able applicants then they've solved the problems of low wages and high-stress conditions. Conversely, we know then that if they can't solve both of those problems, then they won't attract a greater number of able applicants.

Next, we know that if they don't get more able applicants they'll have to either lower entrance standards or we'll suffer a nursing shortage.

Hopefully you can see the connection here: don't solve both problems then won't increase able applicants, which then means lowering standards or nursing shortage.

Finally, we're told that lowering standards or having too few nurses (shortage) would mean the high quality of health care begins to decline.

So this whole thing turns into one big chain:

Not Solve Probs Not More Applicants Lower Standards or Shortage Not High Quality Care

We can also go the other direction with a contrapositive:

High Quality Care Not Lower Standards and No Shortage More Applicants Solve Probs

Those are my quick abbreviations, and yours may be a bit different (see my prior post on why that's okay), but hopefully you captured the logic involved.

At this point all we need to do is move aggressively through the answers to find one that correctly represents any connection shown above. Answer choice (E) represents the first diagram above, where Not Solve Probs starts it and leads all the way down to Not High Quality Care, so that's the correct choice.

In conclusion, there aren't a lot of questions on the test--and there may be none on yours--that require lengthy chains like this, but if you do see one just take it a piece at a time, consider my diagramming advice in the prior post, and see what connections result. As long as you make proper connections and consider contrapositives it should all be fairly straightforward.

Thanks!

[Jon Denning]

Alright, last one!

First off, DEFINITELY memorize those key words! They're triggers that you should recognize as very often indicating conditionality. I say "very often" because obviously English allows for a lot of words to be used in multiple ways, and sometimes they can be conditional and others times not, but still know them and consider them when spotted.

More importantly though are two ideas, both of which you should keep in mind moving forward.

The first is that, judging by where you are in the books, my guess is that you're only just getting started with this idea. So be patient. Like a lot of challenging concepts you need a lot of practice! Fortunately you're going to get tons of it as you get deeper and deeper into the course, and by about lesson 6 or so I imagine this will start to feel much, MUCH more natural. You'll be spotting conditional reasoning immediately and consistently, choosing when and how to diagram appropriately, and making inferences effortlessly. But that only comes with exposure, so stick with it and just press on.

Secondly, conditional reasoning is really a pretty simple idea in principle: whenever two or more things (conditions) are related in an absolute (unchanging, all or nothing) way, you have a conditional relationship. Take the last sentence in question 12 here. There aren't any clear/classic conditional indicator words like "if," "then," "only," "unless," etc, but the relationship in question--shortage of applicants or lowered standards means quality decline--is one given in absolute terms. So it's conditional. And that's about all there is to it!

So to spot conditional reasoning you need to know the classic words, but you must also always be on the lookout for relationships that are constant. The classic words are great at establishing those types of relationships, but they aren't, as we say, necessary What's necessary is just a fixed connection between multiple pieces, however it is that that's described.

Keep at it and you'll find this gets easier and easier as you go.

Thanks!