Differentiating between the sufficient and necessary

[Stephanie Oswalt]

We recently received the following question from a student. An instructor will respond below. Thanks!

Hi,

I'm currently studying for the September LSAT. I've been having problems differentiating between the sufficient condition and necessary condition. I've gone through the various indicators, but I think it would be helpful for me to be able to identify a sufficient condition from a necessary condition without having an indicator to guide me. Do you have any advice on how I can achieve this.

Thanks!
Efe

[Steven Palmer]

Hi Efe,

Conditional reasoning (deciphering between sufficient and necessary conditions) is one of the hardest concepts to grasp while studying for the LSAT. There are a few ways to think about it, and I think one good way is to deeply consider the words themselves: "sufficient" and "necessary". What do these mean?

Sufficient conditions go on the left side of the arrow when we diagram them, which often means students confuse them for causal statements. Instead, a sufficient condition is "sufficient" to tell us something else. In other words, if we know the sufficient condition is happening, then we know the necessary condition must be happening as well. Why? Well, the necessary condition is a requirement ("necessity") for the sufficient condition. Alone, it does not tell us anything, but if it is not happening, then the sufficient condition cannot be happening either. That is the contrapositive.

Another way to look at it is: what condition will definitely inform me of something else? Let's look at an example. A basic conditional statement is "Anyone who has a driver's license must be at least 16 years old." I have two conditions here: having a driver's license (DL) and being at least 16 years old (16+). How do I figure out which condition is sufficient and which is necessary?

Let's pretend we're sitting in a coffee shop and we hear two separate people talking on the phone. One of them (let's call her Mary) says "I just got my driver's license!" to whomever she is speaking. The other person (let's call him Dave) says, to whomever he is speaking, "Wow, I can't believe I'm 25 years old, that's crazy!"

Each of these people has just clued us into one of our two conditions: Mary has her driver's license (DL), and Dave is over 16 years old (16+). Our question now is: which one of these people do I know something else about, based on my rule that "Anyone who has a driver's license must be at least 16 years old." The answer here, is that we know that Mary has her license, and thus has to be over the age of 16. We don't know anything more about Dave, even if he is over 16, since that is a mere requirement of getting a license. The rule would be diagrammed like this:

DL 16+

This is because having a Driver's License is sufficient to know something else: that Mary is at least 16. We know Dave could possibly have his license, since he meets one requirement, but we don't know for sure that he fulfilled the other requirements. Now let's pretend there's a hypothetical third person, let's call her Jen, who is having a phone conversation in our imaginary coffee shop as well. Jen says into her phone, "I just hate being 12 years old, I wish I were older!" Now, what do know about Jen? Jen has not fulfilled a requirement of getting her driver's license, specifically our necessary condition of being at least 16. Based on our contrapositive, diagrammed below, this means she cannot possibly have her license.

16+ DL

I hope this helps!
Steven

[mshaikh]

I am still having the same issue the other student was having! I understand sufficient and necessary conditions in more simple examples but once it starts getting a little more complicated I tend to incorrectly diagram.

For example from my homework in lesson 2, I don't understand these questions and concepts in the sufficient and necessary diagramming drill (here I was supposed to identify the necessary and sufficient condition and diagram that and the contrapositive):

Q: I'll be here until mom picks me up. H = here and MPU = Mom picks up

I diagrammed it like this: H MPU

Now I understand that H should have been crossed off because if the mom picked up I would no longer be here.

How can I avoid confusing these types of sufficient and necessary conditions? How do you know what to negate? When until, unless, and without get added in I get very confused.

Also here is another one I still can't manage to understand.

Q:None but the proud is arrogant.

For this question, how do I even identify the sufficient and necessary condition? I can't figure it out?

Please help!

[mshaikh]

Now looking back at this I understand that the first question can be solved via the Unless Equation.

I am still not sure about this part though:

"Q:None but the proud is arrogant.

For this question, how do I even identify the sufficient and necessary condition? I can't figure it out?"

Also is there a technique to figuring out what the sufficient or necessary conditions are when there are no indicator words?

[Luke Haqq]

Hi mshaikh!

Glad to hear you figured out the first one could be resolved using the Unless Equation! It's a powerful tool for being able to understanding language when the test writers hide conditional reasoning in unclear or indirect sentences. In general, I think it's a good idea just to apply the two rules of the Unless Equation as soon as you see that language (whether "unless" or similar words like "without"). I find it quicker to do this first, rather than try to make sense of the unless-wording on my own. I then approach it in it's "if-then" form, which is easier to understand.

To your other question,

"Q:None but the proud is arrogant.

For this question, how do I even identify the sufficient and necessary condition? I can't figure it out?"

In this conditional reasoning, "none" is functioning identically to "only." That is, another way of saying "none but the proud is arrogant" is to say "only the proud are arrogant." In terms of technique, it's certainly important and can save you time in locating the right answer if you have words like "unless" categorized in your mind. Similarly, if you have the full-length course books, look to the table on page 2-68, "Conditional Reasoning Review Continued." Just like mechanically applying the Unless Equation's rules, having these sufficient- and necessary-condition indicators memorized can be quite helpful.

However, if you detect conditional reasoning but you don't see an indicator word, or perhaps come across words that you're not sure about, the technique I'd recommend again is to try to turn the statement into an if-then statement. If you're not sure which variable goes where, you can try both and see which one makes sense:

(1) P A

or

(2) A P

The first one doesn't seem right, in terms of capturing "only the proud are arrogant." (1) is saying "if a person is proud, then the person is arrogant." But we don't know that "all proud people are arrogant"--that statement would be what (1) carries across. By contrast, (2) means "if a person is arrogant, then that person is proud," which is equivalent to saying "only the proud are arrogant" or "none but the proud is arrogant." And the contrapositive of (2) carries the same meaning: ~P ~A ("if a person is not proud, the person is not arrogant").

In sum, if you're not sure about how to diagram out conditional reasoning when you come across it, try to convert it into an if-then statement. If you're not sure which way to diagram it, try putting one as the sufficient condition and the other as the necessary and try the reverse, seeing which one of those two accurately captures the conditional reasoning.

Hope that helps!

[mshaikh]

Hi Luke,

Thanks so much! This definitely helps. I will apply this strategy each time I don't have indicators.

[LawCraft]

Hi mshaikh!

In sum, if you're not sure about how to diagram out conditional reasoning when you come across it, try to convert it into an if-then statement. If you're not sure which way to diagram it, try putting one as the sufficient condition and the other as the necessary and try the reverse, seeing which one of those two accurately captures the conditional reasoning.

Hope that helps!

How should one apply the if-then statement technique to correctly identify the sufficient and necessary condition in a given prompt without accidentally changing the meaning?

Using "The children go to the park when the sun is shining" as an example from the diagramming drill, the "if-then test" seems to work for either portion of the sentence.

I understand the basic theory of conditional reasoning, but still struggle to identify the correct elements. Furthermore, I am also weak on differentiating the difference between conditional reasoning and casual reasoning. I tend to assume if A occurs, then B follows. I do understand that the order of events may be irrelevant. We just know that "B" must occur, if A does. Is that basically it?

EDIT: I am working on familiarizing myself with the conditional indicators, but I am trying to grasp a better understanding of the theory, so I can be thoughtful when deciding what is sufficient and what is necessary. If I am too formulaic and go off memory, I will likely make a mistake (i.e. fall into some LSAT trap due to odd sentence structure). So, any advice on how to go about it would be helpful. In the above "children go[ing] to the park" example, I recognize that "when" is an indicator word. However, at the time of solving it, I did remember whether this was a necessary or sufficient indicator. In the spirit of tackling these problems on my own and making mistakes now (rather than later), I tried to reason my way to the correct diagram. I frequently get stuck in situations like that and wanted some advice on how to approach conditional reasoning in general.

[Dave Killoran]

Hi LawCraft,

Thanks for the questions! This is a topic that has come up a lot on our forum and blog, and so I'm going to start by referring you to a set of articles to read that I believe will help quite a bit. Then, if you have questions afterwards, just add them here and we'll help you out with them.

For further discussions of conditional reasoning, including an analysis of intuition vs technical knowledge, I'm going to refer you to a variety of resources here that you may find helpful:

• Avoid Real World Interpretations and Follow the Language: http://forum.powerscore.com/lsat/viewto ... p=216#p216
  
  One More Look on what Sufficient and Necessary Means (this is key so that when indicators aren't present, we know what we're doing): http://forum.powerscore.com/lsat/viewto ... 6166#p6166
  
  LSAT Conditional Reasoning: When To Diagram: http://blog.powerscore.com/lsat/bid/333 ... To-Diagram
  
  The PowerScore LSAT Blog, Conditional Reasoning articles - http://blog.powerscore.com/lsat/topic/l ... -reasoning. We write often about this concept, and there are over 20 articles here discussions all sorts of interesting conditional language and arrow relationships.

This is just a small selection of the items we've published on this topic, so I encourage you to go beyond these and explore even more. I frequently write about conditional reasoning since it's so prevalent on the LSAT, so if you search my posts you can find me talking about it quite a bit.

Last note: for now, memorize those indicators and get them down cold. They are like signs on a highway—telling you where to go and what you can do

Please let me know if that helps. Thanks!

[LawCraft]

Hi LawCraft,

Thanks for the questions! This is a topic that has come up a lot on our forum and blog, and so I'm going to start by referring you to a set of articles to read that I believe will help quite a bit. Then, if you have questions afterwards, just add them here and we'll help you out with them.

For further discussions of conditional reasoning, including an analysis of intuition vs technical knowledge, I'm going to refer you to a variety of resources here that you may find helpful:

• Avoid Real World Interpretations and Follow the Language: http://forum.powerscore.com/lsat/viewto ... p=216#p216
  
  One More Look on what Sufficient and Necessary Means (this is key so that when indicators aren't present, we know what we're doing): http://forum.powerscore.com/lsat/viewto ... 6166#p6166
  
  LSAT Conditional Reasoning: When To Diagram: http://blog.powerscore.com/lsat/bid/333 ... To-Diagram
  
  The PowerScore LSAT Blog, Conditional Reasoning articles - http://blog.powerscore.com/lsat/topic/l ... -reasoning. We write often about this concept, and there are over 20 articles here discussions all sorts of interesting conditional language and arrow relationships.

This is just a small selection of the items we've published on this topic, so I encourage you to go beyond these and explore even more. I frequently write about conditional reasoning since it's so prevalent on the LSAT, so if you search my posts you can find me talking about it quite a bit.

LAst note: for now, memorize those indicators and get them down cold. They are like signs on a highway—telling you where to go and what you can do

Please let me know if that helps. Thanks!

Thanks Dave. It's beginning to make more sense. It just seems to not make sense once I encounter a LSAT question.

I will follow up here once I encounter a perfect example during the next homework assignment. I'll work on memorizing the indicator words in the interim.