I just got off a Skype session with a private tutoring student. She's a smart girl, scored 164 on the cold diagnostic assessment. Her Logical Reasoning is good, Reading Comprehension too - but she's terrible at the games.

# Don't let proctors that noisily shell and eat pistachios ruin your test...

We received a couple of emails into the show about proctors making mistakes during the official LSAT. One of them was noisily shelling and eating pistachios and someone else took a couple of phone calls.

People often think we recommend proctored practice tests because of endurance, but that is actually NOT the reason. I'll tell you why we really recommend to do them in the video.

# Stop shooting for a certain number of questions!

# Logic Games Basic Concepts Quiz

Here’s a single-question logic games quiz with a short video explanation. Make sure you understand this principle… it’s incredibly useful for grouping games! Suppose G, H, I, J, and K are about to board Disneyland’s “Splash Mountain.” They are asked to split into a group of two and a group of three. G and H must be in the same group. I and J must be in separate groups.

Can you figure out who goes where? To test yourself, see if you can answer the following question:

Which one of the following must be true?

a) G rides with I. b) H rides with J. c) K rides with J. d) I rides in a group of two. e) K rides in a group of two.

Check out the short video for my solution. (Excerpted from my comprehensive 55-hour online LSAT course.)

# "Necessary and sufficient" for software engineers

The LSAT's big secret is that none of it is really all that hard. Some of the concepts might seem abstract at first, but once you see a few examples you'll usually realize that most of this stuff boils down to common sense. No matter what you studied in school, and no matter what you do for a living, *you're already using these concepts every day*... you just might not realize it.
The email below is from a software engineer who realized that the LSAT terms "sufficient" and "necessary" were simply abstract descriptions of logical processes that he had already mastered. He wrote me to describe his thought process, in the hopes that it might help any other engineering types who are studying for the LSAT.

(Note: For my money, software engineering is a hell of a lot more difficult than the LSAT. If a little code frightens you, feel free to disregard this post. My point isn't that you need to understand this post in order to understand necessary and sufficient. My point is that there are a zillion different ways to understand this concept, depending where you're coming from.)

The letter is from George Yunaev, and it made me very happy. My nerd glee is off the charts right now. Thanks George!

*Would like to share something with you which I created for myself regarding the difference between necessary and sufficient for software engineers.*
*Software engineers might not have a good understanding of formal logic (if any at all), but they do have understanding of how the logical operators work in common programming languages.*

**Necessary condition** means "logical AND". The condition based on A is represented as:

if ( A && X ) // the condition is true else // the condition is false

*Here X is other conditions which value is unknown. What it means that:*

* - If A is false, the result is guaranteed to be false (in fact the computer running this code won't even check X). *
* - However if A is true, the result isn't guaranteed to be true, because now it depends on other value (X) which is unknown.*
*- Therefore based on the value of A we can be only certain when the condition is false, and never certain when it is true.*

**Sufficient** **condition** means "logical OR". The condition based on A is represented as:

if ( A || X ) // the condition is true else // the condition is false

*Same as above, X is other conditions which value is unknown. What it means now that:*

* - If A is true, the result is guaranteed to be true (same way, the computer running this code won't even check X). *
* - However if A is false, the result isn't guaranteed to be false, because now it depends on other value (X) which is unknown.*
*- Therefore based on the value of A we can be only certain when the condition is true, and never certain when it is false.*

*Everyone who knows C, Java, Perl, PHP or even Visual Basic should understand that.*

I don't know any of those languages, or any computer language at all. But I do know that George is right. A sufficient condition means "if X is true, the argument wins... and the argument might be true even if X is false." A necessary condition means "if X is false, the argument loses... and the argument might lose even if X is true."

I love real life examples! Do you have something that worked for you? If so, please share it.

# An LSAT lesson from Dr. Dre

My favorite song is Let Me Ride, from Dr. Dre's studio debut *The Chronic. (*Jesus Christ, was that really 1994?!) There's one verse which I use to teach an important concept about necessary conditions... the fact that there can be *many* of them simultaneously. Seriously... I say this in class. It's a good one!

Dre's in his lowrider, picking up girls. (As usual.) He's on his way to a party, but he's got some important business to take care of first:

**But before I hit the dope spot**
**I gotta get the Chronic**
**The Remy Martin and my soda pop**

Count the necessary conditions:

1) **The Chronic**. Obviously it's not a party without that.

2) **The Remy Martin**. Classy dude.

3) **My soda pop. **Oh, he's cutting it with soda? If I were him, I'd buy cheaper booze.

So here's the LSAT lesson: All THREE of these things are necessary. The failure of any one of these conditions can keep Dre from the party. No Chronic? No party. No Remy Martin? No party. No soda pop? No party.

And it's really important to understand that these three things are *necessary, *but not sufficient. Even if he does have all three of these things, Dre still might not go to the party. There could be other, unmentioned, necessary conditions: Perhaps he's also got to swing by and pick up Snoop Dogg, for example. And he definitely has to avoid getting gatted on the way. Etcetera. So all we know for sure is that if he does make it to the party, he'll be packing all three of these things. If he's lacking any of them, he won't be there. And even if he *does* have all three of them, he still might not make it. That's what "necessary" means.

# What "necessary assumption" means

Yesterday, I discussed one specific type of Assumption question--the "Sufficient Assumption." Today, I'll switch gears and talk about **Necessary Assumptions**. Warning: I'm going to use math again. And once again, if you passed third grade you're going to do just fine.

Premise: Anything times zero equals zero. Conclusion: Therefore A times B is **not** zero.

Question: "Which one of the following is an assumption on which the argument depends?" Or, stated another way, "Which one of the following is necessary support for the argument's conclusion?" Or, stated still another way, "Which one of the following is an assumption required by the argument?"

These three questions are all asking you to do the same thing. Your task is to identify an answer that *must be true*, in order for the argument to even conceivably be true. In other words, it's asking you to identify an answer that, *if untrue*, would cause the argument to fail. In other words, it's asking for a necessary condition.

There are two answers here. "A does not equal zero" is one of them, and "B does not equal zero" is the other. If either of these statements are untrue, then the conclusion of the argument would fail (because anything times zero equals zero). It is **necessary** that A not be zero, and it is **necessary** that B not be zero, because if either A or B are zero, the argument is complete nonsense. Since "A does not equal zero" and "B does not equal zero" were unstated, they are **assumptions**. So "A does not equal zero" and "B does not equal zero" are both **necessary assumptions** of the argument.

Note! Both of these statements are necessary, but neither are sufficient. If A does not equal zero, that doesn't **prove** that A times B is not zero (because B might equal zero). Likewise, if B does not equal zero, that doesn't **prove** that A times B is not zero (because A might equal zero). So neither of these would be correct answers to the question "Which one of the following, if assumed, would allow the conclusion to be properly drawn," which is a sufficient assumption question.

But the questions listed above were all asking for Necessary Assumptions, and "A does not equal zero" and "B does not equal zero" **must be true** or else the argument will fail--thus we know they are "necessary."

The definition of a necessary assumption is "something that must be true, or else the argument will fail." (Alternatively: "something that, if untrue, will prove the argument invalid.") Go ahead and memorize that. Thanks for bearing with my math examples... I'll put away my abacus for a while now.

# What "sufficient assumption" means

Yesterday, I offered a definition of the word "assumption" using a very simplistic mathematical example. Today, I'm going to dig a bit deeper into the Assumption category by using another super-simple bit of math. Don't panic! If you passed third grade, you've seen this math before.

Many students struggle with assumption questions because they don't understand that there are two very different types of assumptions. The purpose of this post is to start teaching you the difference.

The previous post offered an example of an assumption that was both sufficient *and* necessary. Today I am going to talk about just one of those types, the "Sufficient Assumption." So consider the following argument:

Premise: Anything times zero equals zero. Conclusion: Therefore A times B equals zero.

Question: "Which one of the following, if true, would allow the conclusion to be properly inferred?" Or, stated another way, "Which one of the following, if assumed, would justify the argument's conclusion?" Both of these are asking for **sufficient** assumptions. (You might want to memorize the wording of those questions, so that you can differentiate a sufficient assumption question from a necessary assumption question.)

This question is asking you to *prove* the argument's conclusion. In order to prove a conclusion on the LSAT, the conclusion of the argument must be connected, with no gaps, to the evidence offered. So we need an answer that connects the evidence "anything times zero is zero" to the conclusion "A times B is zero."

It's pretty simple. The answer must contain one of the following:

"A equals zero." If it's true that A is zero, and if it's true that anything times zero equals zero, then no matter what B is, the conclusion "A times B equals zero" would be *proven* correct. And proof is what we're looking for on a sufficient assumption question.

"B equals 0" would be just as good, because no matter what A is, the conclusion "A times B equals zero" would be proven correct.

Here's the really interesting part (if you're a nerd like me, which I hope you are). While "A equals zero" and "B equals zero" are each **sufficient** to prove the conclusion correct, neither of these statements, independently, are **necessary **in order for the argument to possibly make sense. A could be 1,000,000, and the conclusion "A times B equals zero" could still be conceivable (if B equals zero). Likewise, B could be 1,000,000 and the conclusion could still be possible (as long as A equals zero.) So if the question had said "which one of the following is an assumption **required by** the argument," (that's asking for a **necessary** component of the argument) then "A equals zero" would *not* be a good answer. Nor would "B equals zero."

The definition of "sufficient assumption" is "something that would prove the argument's conclusion to be correct." Go ahead and memorize that. I'll be back soon to offer a definition of "necessary assumption." Once I'm done with that, I promise I won't use any math for a while.

# What "assumption" means

I came up with this example today while working with a private tutoring student. Consider the following argument:
*A equals two. B equals two. Therefore, A plus B equals four.*

Sounds pretty good, right? Yeah, I think so too. But believe it or not, for LSAT purposes, something's missing. That missing piece is called an *assumption*.

The assumption here is something very obvious, but that's okay. The assumption is* two plus two equals four.*

Yes, I know that everyone knows two plus two equals four. That's beside the point. On the LSAT, every premise should be made explicit if the argument is going to hold water. Same thing with legal writing. As a 1L, I was shocked at how pedantic my Legal Writing instructor wanted my briefs to sound. I've always thought that 1) brevity is a virtue and 2) you shouldn't insult the reader by making points that are too obvious. *This is not how legal writing works. *Less is not more. *More* is more. If your case depends on the proposition that the ocean is wet, you better not leave the words "the ocean is wet" (properly cited to controlling case law, naturally) out of your brief.

Here, the proposition that two plus two equals four is both a necessary and sufficient assumption. I'll explain more about what this means in later posts, but for now, consider this:

**"Two plus two equals four" is a necessary assumption**of the argument because if it's*not*true, the argument loses. If I don't prove that "two plus two equals four", then my opponent might put on an expert witness who says that two plus two equals five. And if two plus two equals five, then A plus B does*not*equal four--it equals five, and I lose my case. (And then I lose my job, for leaving something so elementary out of my case.) Because "two plus two equals four"*must be true*in order for my argument to make sense, it is a necessary component of my argument. Since it was unstated, it is a*necessary assumption*of my argument. If the question had asked "Which one of the following is an assumption on which the argument relies," or "Which one of the following is an assumption required by the argument," then two plus two equals four would be a perfect answer.**"Two plus two equals four" is a sufficient assumption**of the argument because if it*is*true, then my argument wins. There are no other holes in the argument: If it is a fact that A equals two, and also a fact that B equals two, and also a fact that two plus two equals four, then it*must be true*that A plus B equals four, and I win my case. (And then I get promoted.) Because "two plus two equals four" would make it impossible for my conclusion to be false, it is sufficient (*i.e.*enough) to prove my argument. Since it was unstated, it is a*sufficient assumption*of my argument. If the question had asked "Which one of the following, if true, would allow the conclusion to be properly drawn," or "Which one of the following, if assumed, would allow the conclusion of the argument to be properly inferred," or "Which one of the following would justify the argument's conclusion," then two plus two equals four would be a perfect answer.

My student today didn't want to buy the proposition that "two plus two equals four" was an "assumption" of the argument, because he felt "two plus two equals four" was "implied" by the argument, and that it was "too obvious." My response was: "Yes, exactly." Anything that is "implied" by the argument is a very good candidate for an "assumption" of the argument. Likewise, anything that seems "obvious" based on the argument, but isn't actually stated by the argument (or proven by the other premises of the argument) is probably an assumption.

A couple final notes:

- Assumptions are sometimes necessary but not sufficient, sometimes sufficient but not necessary, and sometimes
*both*sufficient and necessary, as in this example. I'll return in later posts with examples of assumptions that are just sufficient and just necessary. - This "two plus two" example is purposely oversimplified. I doubt a real LSAT question (or a real judge) would ever entertain the proposition that two plus two might actually equal five. But "two plus two equals four" is, by definition, an assumption of the argument I made at the beginning of this post. If you need it, and you didn't explicitly state it, then you've just assumed it. And that's a weakness in your argument--a good lawyer isn't going to leave anything to chance.

# The LSAT's dirtiest word

My mom's less than thrilled about it, but my LSAT class, LSAT blog, and LSAT book are all filled with dirty words. I find that sprinkling in a few f-bombs keeps students awake, which is job one when you're teaching 4-hour LSAT classes and spilling tankers of ink on LSAT logical reasoning. (I'll let Mom off the hook here: She certainly didn't teach me to swear. Nope, that would have been my dad. Or more accurately, my dad and his golf buddies, who swear like sailors when they're not at church. Mom, Dad, and Spring Creek Golf & Country Club's many delinquents--I love you all.)
*
*

*Poor Ralphie.*

The purpose of this post is to demystify the LSAT's very dirtiest word, which has a tendency to shock even the hardiest of law school aspirants. It's not four letters--it's six. Cover your ears: The word is "unless."

Let's take a statement from a test I covered last night in class. The September 2006 Official LSAT contained a Logic Game that included the following rule:

"F cannot be selected unless Z is also selected."

Rules that are formulated in this way cause no end of frustration for many LSAT students. My hope is, by the end of this post, to convince you that the word "unless" isn't really all that foul. If you practice enough, you're going to get the hang of it. No need for us all to wash our mouths out with soap.

The rule "F cannot be selected unless Z is also selected" can really only mean one of two things:

**Candidate 1**: F-->Z (if F is selected, then Z is selected.)
Contrapositive: ~~Z~~-->~~F~~ (if Z is not selected, then F cannot be selected.)

or

**Candidate 2**: Z-->F (if Z is selected, then F is selected.)
Contrapositive: ~~F~~-->~~Z~~ (if F is not selected, then Z cannot be selected.)

I don't expect this to be immediately obvious to everyone. But we do use the word "unless" in everyday conversation, so I don't think the use of this word on the LSAT needs to strike such fear in our hearts.

Maybe taking it out of the abstract would help a bit. We don't know F and Z. But we do know Fabio and Catherine Zeta-Jones (the sexiest F and Z I could think of).

*Yeeeeeah, I'm looking at YOU, Fabio. You sexy man. ... Wait, what?*

Okay, imagine if the rule had said "Fabio cannot be at the party unless Catherine Zeta-Jones is at the party." So NOW what do you think the rule means?

**Candidate 1**: Fabio is at the party --> Catherine Zeta-Jones is at the party.
Contrapositive: Catherine Zeta-Jones NOT at party --> Fabio NOT at party.

or

**Candidate 2**: Catherine Zeta-Jones is at the party --> Fabio is at the party.
Contrapositive: Fabio NOT at party --> Catherine Zeta-Jones NOT at party.

Again, the statement was "Fabio cannot be at the party unless Catherine Zeta-Jones is at the party." Time to choose... do you think it's Candidate 1 or Candidate 2?

If Candidate 1 is your answer (F-->Z; ~~Z~~-->~~F~~) then it's okay for Catherine to be at the party by herself, but it's NOT okay for Fabio to be there by himself. (If Fabio's there, then Catherine's there too.)

So this would be okay:

*Yeah... that would definitely be okay.*

and this would also be okay:

*Ooooooh, I didn't think it could get better, but it did.*

This, on the other hand, would NOT be okay:

*Sorry Fabio, you can't get in without Catherine.*

If Candidate 2 is your answer (Z-->F; ~~F~~-->~~Z~~) then it's okay for Fabio to be at the party by himself, but it's NOT okay for Catherine to be there by herself. (If Catherine's there, then Fabio's there too.) So this would be okay:

*Nice.*

and this would be okay too:

*Yeah, that's VERY nice.*

But this would NOT be okay:

*Where's the sexy man with the vest?*

One last time: The rule is, "Fabio cannot be at the party unless Catherine Zeta-Jones is at the party."

Time for the answer:

The winner is **Candidate 1**. The statement "Fabio cannot be at the party unless Catherine Zeta-Jones is at the party" simply means "if Fabio is there, then Catherine has to be there too": F-->Z; ~~Z~~-->~~F~~. Catherine's presence is *necessary* for in order for Fabio to be there. And if Fabio is there, that's *sufficient information* for us to know that Catherine has to be there too.

It's okay if this is still a bit puzzling--I'll be back in my next post with a boatload of additional "unless" examples. For now, see if personalizing it (as I've done above, taking it out of the abstract by using well-known celebrities) helps you understand an "unless" statement. I really don't think this is the kind of thing that can be understood by any formula or memorization technique. We use the word unless all the time in real life. Just like swear words, it's nothing to get worked up about. I'll be back soon with more.

# If *and* only if

Yesterday, I spent some time discussing the difference between "if" and "only if." We learned that "I'll go to your party IF Miguel goes" is not the same as "I'll go to your party ONLY IF Miguel goes," for LSAT purposes. Today we'll discuss the statement "I'll go to your party IF AND ONLY IF Miguel goes," because this means something different than both of the prior statements. You might need to memorize this. "If and only if" means that BOTH rules ("I'll go IF Miguel goes," and "I'll go ONLY IF Miguel goes") are simultaneously in effect. What this means is that Miguel is both a sufficient condition AND a necessary condition for my attendance. As we discussed yesterday,

"I'll go IF Miguel goes" indicates that Miguel is a sufficient condition for my attendance. If Miguel is there, then I'm definitely going to be there.

"I'll go ONLY IF Miguel goes" indicates that Miguel is a necessary condition for my attendance. If Miguel is not there, then I'm definitely not going to be there.

"I'll go IF AND ONLY IF Miguel goes" indicates that both of these rules are in effect. So you'll either see both of us at your party or neither of us at your party--you definitely won't see either of us there alone.

To diagram this statement, you can do one of two things. First, you could simply put both rules in effect:

M-->N (I'll go if Miguel goes.)

~~N~~-->~~M~~ (Contrapositive)

N-->M (I'll go only if Miguel goes.)

~~M~~-->~~N~~ (Contrapositive)

If you write all that, you'll have correctly captured all the implications of the "if and only if" rule.

Or, you can simply make the arrow go both ways. Note that "If and only if" is the ONLY time you can allow the arrow to go both ways. The diagram would look like this:

M<-->N (I'll go if and only if Miguel goes.)

~~N~~<-->~~M~~ (Contrapositive)

Take a deep breath--we're almost done with our discussion of the basics of LSAT arcana. Fortunately for people with bad memories like mine, there aren't that many things to memorize. Once you've got these basics down, it'll just be a matter of practice.

In later posts, I'll talk about the use of "unless" as it pertains to the LSAT, and the practice of linking conditional statements together. As always, I promise that it's easier than it looks at first blush. Send me an email, or pick up the telephone--I'm always happy to provide additional examples. And for tons more written examples--using actual LSAT questions--of everything I discuss on the blog, check out my book: Cheating the LSAT.

# "If" vs. "only if"

Imagine you invited me to a party. I could be a polite guest and simply say "Yes, I'll be there," or "I'm sorry, I have a prior obligation." Either of those responses would make it easy for you--you'd know for sure whether or not you should plan on me. But I could also be a pain in the ass and put a *condition* on my attendance. I could say, "I'll go *if* Miguel Angel Jimenez goes." Or I could say, "I'll go *only if* Miguel Angel Jimenez goes." In real life, those two statements might sound like the same thing--you'd try to figure out whether Miguel is coming, and then you'd know whether or not I'll be there. But on the LSAT, it's more complicated than that. The two statements do *not* mean the same thing on the LSAT--they mean subtly, yet concretely, different things. The purpose of this post is to explain that difference, because it's a critical concept.

*Miguel Angel Jimenez: The most interesting golfer in the world.*

If I say "I'll go if Miguel goes," what I'm telling you is that Miguel is a "sufficient condition" for my attendance. If Miguel is there, that's *sufficient information* for you to know that I will also be there. Memorize this: **The word "if," on the LSAT, indicates a sufficient condition. **So "I'll go if Miguel goes" looks like this:

M --> N

This does not, of course, mean that if I go Miguel must also go. The arrow only goes one way! What it *does* mean is that if I'm not there, Miguel can't be there:

~~N~~ -->~~M~~

(What I just did there is called the "contrapositive." If you're having any trouble following so far, please check out my posts on the sufficient and necessary conditions.)

Now, I need you to carefully consider what this actually means:

- It's okay for Miguel and Nathan to both be at the party.
- It's okay for neither Miguel nor Nathan to be at the party.
- It's okay for Nathan to be there without Miguel. (I said I'd go if Miguel goes... but I didn't say I wouldn't go without him!)
- But it's NOT okay for Miguel to be there without Nathan. I told you that I'd be there if Miguel was there. So if Miguel is there and I'm absent, then I've broken my promise to you.

This might all seem obvious so far. But the next step is where your mind will be blown, so please pay careful attention.

If I say "I'll go **only if** Miguel goes," (or "I'll **only** go if Miguel goes,") I'm no longer telling you that Miguel is a sufficient condition for my attendance, like I was in the discussion above. Rather, I'm telling you that Miguel is a *necessary* condition: If I'm there, then Miguel is also going to be there. **Memorize this: "Only" indicates a necessary condition.** So "I'll go only if Miguel goes looks like this:

N --> M

This does not mean that if Miguel goes I must also go. The arrow only goes one way! What it *does* mean is that if Miguel is not there, I can't be there:

~~M~~ -->~~N~~

(I just did the contrapositive again. And, reminder, if you're having trouble following the discussion it really might help to check out my posts on the sufficient and necessary conditions.)

Now, I need you to carefully consider what this actually means:

- It's okay for Miguel and Nathan to both be at the party.
- It's okay for neither Miguel nor Nathan to be at the party.
- It's okay for Miguel to be there without Nathan. (I said I'd
**only**go if Miguel goes... but that doesn't preclude me from skipping the party even if he's there!) - But it's NOT okay for Nathan to be there without Miguel. I told you that I'd
**only**be there if Miguel was there. So if Miguel is absent and I'm there, then I've broken my promise to you.

To recap:

**In both scenarios**, it's okay for both Miguel and Nathan to be at the party.

**In both scenarios**, it's okay for both Miguel and Nathan to be absent from the party.

**In the "I'll be there if Miguel is there" scenario**, it's okay for Nathan to be there without Miguel, but it is not okay for Miguel to be there without Nathan.

**In the "I'll only be there if Miguel is there" scenario**, it's okay for Miguel to be there without Nathan, but it's not okay for Nathan to be there without Miguel.

Please note the difference between the last two outcomes. This is a departure from how people tend to talk in everyday life, so it's something that you might just need to memorize for the LSAT.

One last note, if your head is spinning: This concept is a lot easier than it might look at first! Please email me with questions, or talk to me in class, and I'll be happy to walk you through it and provide additional examples. As always, I'm here to help.

Best,

--nathan

# What "necessary" Means

Yesterday, I discussed the concept of sufficiency via a few examples. Today, I'll discuss the concept of necessity using those same examples. What does it mean for something to be "necessary"?

The first example I gave yesterday was this:

"If I get the loan, then I promise to buy your house."

This means that IF the loan is granted, then it is NECESSARY to buy the house. You can't get the loan without being obligated to buy the house. This doesn't mean that if you don't get the loan you can't still buy the house, or be obligated to buy the house for some other reason. What it DOES mean is that if you're not obligated to buy the house, then you didn't get the loan. Again: buying the house is NECESSARY if you get the loan.

**Memorize this: The necessary condition is always on the right. **So the statement above could be diagrammed like this:

Get loan --> Buy house

And the contrapositive (a concept I introduced yesterday) is this:

~~Buy house~~ --> ~~Get loan~~

- So getting the loan is
*sufficient information*to prove that you have to buy the house. - Another way of saying this is that buying the house is
*necessary*if you get the loan. - Another way of saying this is that if you don't buy the house, that's
*sufficient information*to prove you didn't get the loan. - Yet another way of saying this is that not getting the loan is
*necessary*if you don't buy the house.

The four statements above are all logically identical.

We can do the same thing with the other two examples I gave yesterday:

"If you're Warren Buffett, then you're rich."

Since the necessary condition is always on the right, that looks like this:

Buffett --> Rich

and the contrapositive:

~~Rich~~ --> ~~Buffett~~

- So being Buffett is
*sufficient information*to prove that you are rich. - Another way of saying this is that being rich is
*necessary*if you are Buffett. - Another way of saying this is that if you aren't rich, that's
*sufficient information*to prove you aren't Buffett. - Yet another way of saying this is that being someone other than Buffett is
*necessary*if you aren't rich.

The four statements above are all logically identical.

And the final example I discussed yesterday was:

“If you trip and fall headfirst into an industrial sausage grinder, then you are dead.”

Since the necessary condition is always on the right, that looks like this:

Sausage Grinder --> Dead

And the contrapositive:

~~Dead~~ --> ~~Sausage Grinder~~

- So going into the grinder is
*sufficient information*to prove that you are dead. - Another way of saying this is that being dead is
*necessary*if you go into the grinder. - Another way of saying this is that if you aren't dead, that's
*sufficient information*to prove you didn't go into the grinder. - Yet another way of saying this is that having stayed out of the grinder is
*necessary*if you aren't dead.

The four statements above are all logically identical.

More than anything, I promise you that this is all a hell of a lot easier than it might look at first blush. If you have questions, I really hope you'll post them here.

Next time, I'll be back with a look at the very big difference between "if" and "only if."

# What "sufficient" means

One of the most basic concepts on the LSAT is the idea of conditional statements. The simplest form is a straightforward if-then statement. In a contract, it might look like this: "I promise that if I am approved for the loan, then I will buy your house."

This promise means that if you get the loan, we have *sufficient information* to know that you are contractually obligated to buy the house. And if you don't get the loan, then we have sufficient information to know that you're *not* obligated to buy the house. This is super-important: The promise only applies IF you are approved for the loan. If you're NOT approved for the loan, the promise has no effect whatsoever--it's as if the promise doesn't even exist. Even if you're turned down for the loan, you could still buy the house. Maybe you win the lottery, maybe you find $500,000 under your mattress, whatever--your promise to buy the house if you DO get the loan does not prevent you from buying the house through some other means if you DON'T get the loan.

Here's another simple example:

"If you're Warren Buffett, then you're rich."

This statement means that if you ARE Warren Buffett, then we have sufficient information to know that you are rich. (Buffet-->Rich). What the statement *doesn't* mean is that anyone who is rich is Warren Buffett. There are plenty of other rich folks in the world. But the statement *does* mean that if you're NOT rich, then you are NOT Warren Buffet. (NOT Rich-->NOT Buffet).

What I just did there is called the "contrapositive." Memorize this: **To do the contrapositive, you must 1) switch the order of the terms, and 2) negate the terms. **It's very puzzling to new students, but pretty straightforward once you get used to it.

Another example:

"If you trip and fall headfirst into an industrial sausage grinder, then you are dead."

Okay, so if someone gets turned into sausage, that's *sufficient information* for us to know that they are dead. (Sausage-->Dead). But that doesn't mean that every dead person fell headfirst into an industrial sausage grinder. The arrow only goes one way. What it *does* mean is that if you are NOT dead, then you could NOT have fallen into an industrial sausage grinder. When we draw the contrapositive, we'll see the terms in 1) opposite order with 2) the opposite sign. So the contrapositive is (NOT dead-->NOT sausage). If someone is NOT dead, then we have *sufficient information* to know that they are not sausage.

Also memorize this: **The sufficient condition is always on the left. **Next time, I'll revisit this same concept and introduce the term "necessary."