We deal with "if-then" statements all the time in everyday life. "If I have another drink or two, I won't be able to drive safely." "If I get a higher LSAT score, I'll be competitive at better law schools."The LSAT Logical Reasoning section requires us to think about these statements a little more formally than we're used to. (If we want to do well on the LSAT's Logical Reasoning section, we'll have to think about these statements more formally.)
This blog post will explain "sufficient" and "necessary" and describe them with a few examples.
The "sufficient" condition is often introduced by words such as "if," "when," and "whenever."
Something that's sufficient is enough to get the job done. However, without more info, we can't assume that it's a requirement (necessary).
It might help to think of the sufficient condition as "activating" the necessary condition.
The "necessary" condition is often introduced by words such as "then," "must," and "required."
Something that's necessary has to happen in order for the "sufficient condition" to occur.
However, without more info, we can't assume that it's the only thing that has to happen in order to know that the sufficient condition also happened (or will happen).
Here are a few examples of the sufficient and necessary conditions in action:
Limos
"If I take a limo, I'll get where I want to go."
A limo would be sufficient to get me wherever I want to go.
However, I don't need fancy forms of transportation. There are other ways to get to where I need to go - I could walk, run, bike, or take the subway, bus, or a taxi.
(In fact, I'd prefer a helicopter or rocket ship over a limo if I had my pick.)
Un-friending on Facebook
"If we break up, I'll un-friend him/her on Facebook."
Breaking up might be sufficient to un-friend a significant other, but breaking up isn't required (necessary) to un-friend him/her.
You might un-friend him/her in the middle of a fight without actually breaking up.
Becoming President
"If you have a reasonable chance of becoming President of the United States, then you must be affiliated with one of the two major political parties."
However, being affiliated with the Democrats or Republicans is not enough to become President. You also need to win your party's nomination and, eventually, the Electoral College.
***
For more Logical Reasoning fun, check out Conditional Reasoning: Contrapositive, Mistaken Reversal, Mistaken Negation and Formal vs. Informal Logic in LSAT Logical Reasoning.
Photo by muckster / CC BY-NC-SA 2.0
I was reading Slate's interview with Peter Orszag (the director of the Office of Management and Budget from the White House) and I came across this:
ReplyDeleteFor example, CBO doesn't see electronic health records as producing significant budgetary savings in the near term. Even so, nobody—not IOM, not CBO, not me—thinks that we can achieve higher-quality, lower-cost health care without the widespread adoption of health information technology. **(That is, health information technology may not be sufficient for moving us to a higher-quality lower-cost system, but it is necessary.)** (asterisks mine)
Needless to say, in an interview about the fate of health care reform, one of the most significant and far reaching issues of my generation, I was most overjoyed when I saw sufficient and necessary conditions referenced.
...I...I might be studying too much?
2 months in, and I still don't fully grasp the terms "sufficient" and "necessary." I get questions right, and I understand the relationship in conditional statements, but I just don't like the actual words themselves.
ReplyDelete"If I take a limo (to my next free LSAT Logic Games workshop, for example), I'll get where I want to go."
Get to where I want to go is necessary? Huh? It's necessary to get where you want to go? I see that a limo would be "sufficient." It would get the job done. So would other things. What's necessary? Necessary should be something like "the act of moving to a desired location." THAT is 'necessary' to get where you want to go. "where you want to go" is NOTHING. Necessary my ass.
I want new words. Or, for someone to explain this in a way that actually penetrates the hollow titanium ball I call my skull.
I think I have a good example that helps me understand it and I think is correct. If you're trying to open a door that has two locks, it's safe to say that you need both keys in order to open it. It is NECESSARY to have key #1 in order to open the door. However, it is not SUFFICIENT because you need both keys. What NECESSARY implies is that if you don't have key #1, you cannot open the door. So if you have Key #1 then I'm still not sure whether you can open the door or not. But if you don't have Key #1 then I'm sure you cannot open the door. Does that make sense?
DeleteI think you guys are making the cardinal mistake of adding information that has not been provided. The only information you are given is:
Delete"If I take a limo, I will get where I want to go." This is ALL you know!
So, ask yourself, with ONLY this information what is NECESSARY to happen?
What is necessary - from this information ONLY - is that by taking a limo I will get where I want to go. That's the information you have been given: I take a limo, I MUST get to where I want to go. There is no provision for taking a limo but not getting to where I want to go. So according to what has been provided, I will NECESSARILY get to where I want to go if I take a limo!
What is NOT necessary is that if I got where I wanted to go, I had to have taken a limo. This provision has NOT been provided. Thus, taking a limo is the SUFFICIENT condition by default (I.e., you will always have both, so if you identify one the other is...the other). ;)
I find it generally easier to use this method, i.e., first identify the NECESSARY condition - what must happen given the information provided - and then the SUFFICIENT condition is known by default, rather than try to identify the SUFFICIENT condition. SUFFICIENT is always a little harder to conceptualize, I think.
Hope this helps!
Sooooooooooo agree with Caleb. I get the whole sufficient thing - the 'it is enough to establish that...' But NOT the necessary. If you don't need a limo to get there, and you can get there by other means, why is getting where I want to go the necessary.
ReplyDelete"If you are red/green color-blind, you can't distinguish between green and brown"
Being red/green color-blind is enough to establish that you can't distinguish between green and brown, but distinguishing between green and brown is NOT necessary - it isn't enough to being color-blind. It doesn't mean you are color blind. I DON'T FRIGGIN GET IT.
"If you are red/green color-blind, you can't distinguish between green and brown".
DeleteThis could actually be an if-and-only-if statement and still be true. Not being able to distinguish between green and brown IS a necessary condition for being red/green colour-blind (assuming that your example statement is true). Why? You just have to negate the condition that you think might be a necessary condition and see if that guarantees the negation of the condition for which you think the examined condition is necessary. In this case, doing this would mean thinking about what happens when you CAN distinguish between green and brown. Does this guarantee that you're NOT red/green colour-blind? Yes, therefore, not being able to distinguish between green and brown is a necessary condition for being red/green colour-blind, for if you ARE able to distinguish between green and brow (the negation of the putative necessary condition), then you are NOT red/green colour-blind.
What he means is that, a limo is an option that you could use to get complete the sufficient condition. The LSAT tells you what the necessary condition is, and that this necessary condition is TRUE. So all other options of the way in which to have gotten the LSAT book are not. If you got your LSAT book, then you had taken a limo (yes, there're many other ways to complete this task, but when you're told this on the lsat, THAT IS THE WAY THE BOOK WAS PROCURED. however, you can't reverse to incorrectly to say, "if you took a limo, you got your lsat book." in the same way as all necessary vs sufficient condition statements, "if you didn't take a limo, then you didn't get your lsat book," would be the contrapositive.
ReplyDeleteDon't think of it as, "but there're are a million other ways for the sufficient condition to be met in the physical world," think of it as the exam telling you, "that THIS is the way the sufficient condition is to be met."
It seems the more this is tried to be explained, the more confusing it gets!
ReplyDeleteI agree with Caleb and Anonymous. I understand it in the conditional statements, but trying to understand it in real life??? Not going to happen in the near future!
Hi Marsha,
DeleteHere's the one in real life.
Necessary: Having the correct key is NECESSARY to, in a normal manner, enter one's own apartment.
(You can't enter your apartment without the correct key. I think is very closely related with real life. In this case, having the correct key is the MUST condition, which is same as NECESSARY.)
It is trick to provide an example with sufficient since there are so many counter conditions that may break it. So, for now, try to see is this necessary example make sense to you.
Hope this is helpful.
Tianyu Ma
One example:
ReplyDeleteIf your goal is to get a girlfriend, then a NECESSARY condition would be that you talk to a girl. This makes sense because you cannot get a girlfriend without every having talked with a girl.
However, talking with a girl is not a SUFFICIENT condition, because it does not automatically get you a girlfriend. In other words, you must talk with a girl in order to get a girlfriend, but that does not guarantee that you will succeed.
A SUFFICIENT condition for getting a girlfriend could be going to a bar, talking with a girl, and then having her agree to go out with you. This is SUFFICIENT because it accomplishes the goal. However, this instance in particular is not NECESSARY because there are other methods for getting a girlfriend.
I completely agree with all of y'all. I have been at this for months! I can answer the questions correctly for the most part but it really irritates me that I still do not fully grasp the necessary condition. Like you've all said, the "sufficient" condition is easy to grasp. If I save enough money, then I will go an exotic vacation. Saving money is sufficient to go on the vacation though I don't necessarily need to go on this vacation even if I've saved all the money in the world. Perhaps I'll save the money for law school instead. Furthermore, maybe my rich friend pays for my exotic trip and I can go without having saved money or if I had saved money, then I can both put it away for law school and go on an exotic trip. Why can't the necessary condition ever be explained in a way that makes sense to me.
ReplyDeleteSTEVE? ANY THOUGHTS?
Part of the problem could be the understandable confusion when using both the term "sufficient" and the term "necessary" when discussing conditionals that use "if-then." The following might help clear this up.
DeleteExample: If I save enough money, then I will go on an exotic vacation.
According to one of Steve's explanations
(http://lsatblog.blogspot.com/2009/10/words-indicating-sufficient-necessary.html), it seems that any conditional statement using "if-then" contains two conditions: (1) a sufficient condition; and (2) a necessary condition.
However, it appears that the "necessary" condition in a conditional statement using "if-then" is different from the "necessary" condition in a conditional statement using "only-if."
"If I save enough money" -- the sufficient condition
"then I will go on an exotic vacation -- Why is this condition "necessary"? Well, going on an exotic vacation is "necessary" in this case because it automatically follows from A. If you have A, then you will have B. As someone else posted, B has no choice in what happens. B follows automatically (necessarily) because you have A. So B is a necessary consequence of A. That is what makes "going on an exotic vacation" a necessary condition, i.e., this condition follows necessarily from having A.
In contrast, a "necessary" condition in a conditional using "only-if" could be seen as a second, different type of "necessary" condition.
Example: I will go on an exotic vacation only if I save enough money.
Here, "if I save enough money" is the "necessary" condition for going on an exotic vacation. This second, different type of "necessary" condition does not automatically follow from anything. Saving enough money is necessary for another condition, but saving money does not by itself lead to that other condition.
So in the first example, "If I save enough money" functions as a sufficient condition, and in the second example, "if I save enough money" functions as a necessary condition.
Similarly, in the first example, "then I will go on an exotic vacation" is the necessary condition (it automatically follows from saving enough money), and in the second example "I will go on an exotic vacation" is the condition FOR WHICH a necessary condition (saving enough money) is stated.
The fact that "going on an exotic vacation" is a necessary condition (or necessary consequence) in the first example can also be illustrated by looking at the contrapositive. If I save enough money, then it is a necessary consequence that I go on an exotic vacation. Contrapositive: I did not go on an exotic vacation, and therefore, I did not save enough money. If I had saved enough money, then it would have automatically followed that I went on an exotic vacation. But I didn't go on that vacation, so I couldn't have saved enough money to do so. Whew.
Another interesting point about "if-then" and "only-if" statements.
DeleteI will go on an exotic vacation only if I have saved enough money.
If I will go on an exotic vacation, then it means that I have saved enough money.
The first example's "necessary" condition for going on an exotic vacation becomes the second example's "necessary" consequence.
The condition for which a necessary condition is given in the first example becomes a sufficient condition in the second example.
So an "only-if" statement can be turned into an "if-then" statement, but the roles played by the two parts change.
Cubria (and anyone else having difficulty understanding lsat logic), not sure if this'll help, but try thinking about it this way...
ReplyDeleteYou are completely right that there are plenty of ways (including saving money or not) for you to go on vacation or not go on vacation, BUT...
my understanding is that when the lsat gives you a necessary condition, THEY OFTENTIMES (IF NOT ALWAYS) MAKE IT UP TO GO ALONG WITH THE SUFFICIENT. and you have to work with it. period.
so for example if the lsat told you, "If Cubria saves up $2000 she will go on vacation to Brazil," then you have to work with that conditional statement in finding the answer. The fact that you could go to Brazil in reality whether or not you saved up $2000 is completely valid and makes sense IN REALITY. but in the lsat world the necessary condition is just something the lsat typically makes up to go along with a sufficient to test your ability of understanding the logic behind the question.
Stripped down to a basic core, a question might then ask: Which of the following must be false?
CORRECT ANSWER: Cubria chose to sit at home and not go to Brazil even though she saved up $2000.
That's false because the stimulus said that if Cubria saves up $2000, she's gotta hop on a plane and head on down for some Caipirinhas.
It just dawned on me and makes complete sense now:
ReplyDeleteA sufficient condition is one thing you could do to get your goal completed. It's sufficient to get the job done.
e.g. A limo is sufficient to get me to the testing center, but it isn't necessary because I can take a cab or the bus.
A necessary condition is one thing that is required to get your goal completed, but alone it is not sufficient to get the job done.
Being affiliated with the democratic or republican is necessary to become President, but alone it is not sufficient to become President. One needs to win the party's nomination, and be elected by the people.
I hope this helps. It just clicked for me and it feels great!
Hi Steve,
ReplyDeleteI was talking with (precisely, texting) a friend tonight and after having done too many logic games lately, I found myself trying to decipher the things I said/thought into sufficient/necessary clauses. This is how my conversation with my friend, Sam went:
Me: Don’t tell me you're a Twilight fan!
Sam: Hell, no! I’m too manly for that!
Almost automatically, the following question popped up in my LG-overloaded brain:
"Hey, even if you’re manly, you could still be a Twilight fan! And if you are a Twilight fan, it doesn’t necessarily mean you’re not manly."
So here's what I was trying to ask myself: within those two sentences that popped up in my head,
Q1: Which clause is the sufficient clause, and which is the necessary one?
Q2: What are the contrapositives of both statements?
For “And if you are a Twilight fan, it doesn’t necessarily mean you’re not manly."
I tried “If you are a Twilight fan, you could be either manly or girly.” Hence, the "if" clause is the sufficient one, and the other one necessary.
However, the sentences didn’t seem to have such clear-cut sufficient/necessary clauses. So then I figured that Sam’s statement was based on the assumption that “If you are a Twilight fan, then you’re not manly.” And the contrapositive of that statement is, “If you’re manly, then you are not a Twilight fan.”
In other words, if Sam’s assumption were true, then he would have proved my two statements wrong.
What do you think? Is there any possible way of answering my two questions above though?
[and for all those who have noticed themselves doing the same thing while talking to other people, it's a good sign- that the LSAT has infiltrated your brain]
Thanks!
Need some help. How would the following statement be diagrammed?
ReplyDelete"Since no pigs have wings."
Thanks.
~P&W
ReplyDeletemaybe? :-) just started, trying to follow along...
If A, then B. B, only if A. I think that's how it would go. Not "If A, then B. A, only if B." That's why I was flummoxed about the whole thing. Now I have figured out why I couldn't get it before. Makes more sense to me,,,,
ReplyDeleteFirst:
If I get a raise (A), then I can afford to move to a nicer place (B).
A is the necessary condition in order to obtain the desired result.
Contrapositive: If I don't get a raise, then I can't afford to move to a nicer place.
So: When I DO move to a nicer place (B), it's BECAUSE I got the raise (A).
Or: When I don't move to a nicer place (B), it's BECAUSE I didn't get a raise (A).
Second:
I can afford to move to a nicer place (B) ONLY IF I get a raise (A).
"A" is the necessary condition in this statement, too.
Contrapositive: I can't afford to move to a nicer place if I don't get a raise.
I moved to a nicer place BECAUSE I got a nice, fat raise.
If I am the President of the United States, then I was born in the U.S. You can infer that because I am President, I was born here. But contrapositive doesn't work: If I am NOT the Pres, then I was NOT born in the U.S. What gives?
You're denying the antecedent (negating the sufficient condition) which is a logical fallacy.
Deleteif P -> US
contrapositive should read ~US -> ~P or "If I'm not born in the US then I can't be president."
Very cool! Loved the Facebook example, it's great when you give silly everyday examples- they are always the examples (and concepts) that I remember best because the examples stick-out and are therefore, memorable! Thank You!
ReplyDeleteIt seems to me that all this confusion arises because it's not explained that "A condition A is necessary for a condition B" and "A condition A is sufficient for a condition B" are both a conditional statement and absolutely nothing more. All this language about necessary and sufficient conditions is pure rhetoric for the same fundamental idea: A conditional statement.
ReplyDelete"A condition (situation, occurrence, event) A is sufficient for a condition (situation, occurrence, event) B" EXACTLY means "If A occurs, B (will) occurs for sure", or "Whenever A occurs, B (will) always occurs".
"A condition (situation, occurrence, event) A is necessary for a condition (situation, occurrence, event) B" EXACTLY means "If A doesn't occur, B won't/doesn't occur for sure", or "Whenever A doesn't occur, B (will) never occurs". A necessary condition is NOTHING more than this.