In conditional statements (if-then) statements, the sufficient condition is the one that goes before the arrow, and the necessary condition is the one that goes after the arrow.Sufficient ---> Necessary
X ---> Y
is equivalent to:
if X, then Y.
X is the sufficient condition, and Y is the necessary condition.
Logic Games and Logical Reasoning contain conditional statements most prominently, but you can also find them in Reading Comp.
First, some words that indicate each type of condition.
Sufficient (before the arrow):
All, any, every, if, in order to, the only, to be, when, whenever
Necessary (after the arrow):
depends upon, must, only, only if, only when, requires, then
I like to think of the relationship between sufficient and necessary conditions in the following 2 ways:
Way #1: the sufficient condition activates the necessary condition, indicating that it will happen.
Way #2: the sufficient condition is enough to guarantee that the necessary condition happened already.
If the sufficient condition occurs, then the necessary condition must also occur (Way #1), or it must have also occurred at some point (Way #2). Yes, that's right, in Way #2, the necessary condition might occur before the sufficient condition.
I can hear some of you saying, "How could such a thing happen? If the necessary condition appears after the sufficient condition in a sentence, it must occur after the sufficient condition in real life too!"
Not so. But first, let's deal with the easier way (Way #1):
---
The sufficient condition can occur before the necessary condition (Way #1):
If A occurs, then B must occur afterwards.
For example, if I slam my head into a brick wall, then my head will hurt.
This could also be phrased, "Whenever I slam my head into a brick wall, my head hurts."
(A = slam head, B=head hurting)
If we take the contrapositive of this statement, we can say:
If my head doesn't hurt (NOT B), then I must not have slammed it into a brick wall (NOT A).
---
However, the sufficient condition can also occur after the necessary condition (Way #2):
If C occurs, then D must have already occurred.
For example, if I seduce an LSAC employee to get an advance copy of the LSAT, I must have traveled to LSAC's headquarters in Newtown, Pennsylvania.
(C= Seducing LSAT's test-writers, D=traveled to LSAC HQ in Newtown, PA)
This means that if you see me in NYC, I must not be seducing an LSAC employee at the moment.
(I know I'm going to get some emails requesting an advance copy of the LSAT, so I'll tell you right now - that sentence was a joke.)
***
Also see LSAT Logic | Necessary vs Sufficient Conditions.
Photo by alltheaces / CC BY-NC-ND 2.0
I was trying to come up with an example for "the only" as a sufficient condition indicator but was unable to. Is "the only" not a necessary condition indicator?
ReplyDeleteFor example,
The only time I woke up before 5 a.m was when I took the LSAT.
Here, "the only" relates to when I took the LSAT. The sentence could be re-written as "If I had woken up before 5 a.m. then I must have been taking the LSAT that day".
Could you please clarify? Thank you :)
Hi Pax,
ReplyDelete"The only" is a sufficient condition indicator.
Example:
"The only girls I date are models."
This means:
If I date a girl, she must be a model.
Your sentence above, in if-then format, should be:
If I woke up before 5AM, it must have been to take the LSAT.
Your rewritten version is incorrect - it's a mistaken reversal.
Hope this helps!
....aaah! now I see it!
ReplyDeleteThank you Steve.
Hey--I grew up two towns over from Newtown (and worked there for a while too). It's one of the cutest little towns ever! I never even knew that the LSAC hq are there...weird.
ReplyDeleteI like those explanations, particularly because they reference the influence (or relative lack thereof) of time. I like to think of the sufficient and necessary as actors (though only in the most twisted of terms with regard to their ability to entertain):
ReplyDeleteThe sufficient condition can do anything it wants, regardless if the necessary occurs. However, if the necessary occurred, we can suffice that it is only necessary that the sufficient occurred...Right?
Although this was an old comment, I don't think this is correct. In fact, I think it's confused the conditions.
DeleteRather, the necessary condition can do anything it wants, regardless if the sufficient occurs. However, if the sufficient occurred, we can suffice that it is only necessary that the necessary occurred. (By the way, that last sentence is incredibly redundant but I'm just trying to use the same language. Simplified, if the sufficient occurred, then the necessary condition must occur.)
A Mistaken Reversal for visual learners:
ReplyDeletehttp://comixed.memebase.com/2010/11/12/4-koma-comic-strip-drawing-a-logical-conclusion/
taken from the comments:
ReplyDelete"The implication is that since MJ went from being a black boy to a white lady, Beiber will go from being a white girl to a black man."
The reasoning is flawed because it....
ReplyDelete..treats two cases as being similar that are different in a critical respect..
I have a question about the Way #2 example. The contrapositive you give for the example is (as I understand it): "If you see me in NYC, I must not be in Philadelphia at the moment." Let's pretend that the question - based on this example - is something like:
ReplyDeleteIf Jane had seduced an LSAC employee, she would have gone to Newtown, Philadelphia. Jane is in NYC at the moment, so Jane did not seduce an LSAC employee.
Isn't that example a necessarily flawed one? Just because Jane is not currently in Newtown, doesn't mean that she never went to Newtown. Or am I missing something? Is this example phrased as such on purpose - i.e. would this be an example of a "flaw" LR question?
Thanks!
Susan, I was wondering the same thing. Just because you are currently in NYC, does that necessarily mean you weren't recently in Newtown seducing an LSAC employee? I wouldn't imagine so. Is there possibly supposed to be an assumption that you were in NYC at the expense of said trip to Newtown?
ReplyDeleteThanks!
Steve specified that at the moment he is in NYC, then at that moment he is not in Newtown.
ReplyDeleteHi Steve,
ReplyDeleteDoes "If only" introduce a sufficient condition? "If only I had enough time I would go to the movies." Would this sentence be diagrammed as [Enough time --> Go to the movies]?
Yes. "If only" introduces a sufficient condition. Don't let the "only" part fool you; it actually is irrelevent. The only important part, in terms of triggering a sufficient condition, is "if". Your example could just as well have "only" removed and it wouldn't change the meaning.
Delete"If" = succificent; "only" = necessary. Just remember that and try to ignore what comes after. So for example, "only if" = necessary, "if only" = sufficient, both on account of the first word in the phrase.
Hope that helps.
Excellent point. How about, "if and only if..."? In that case you have a situation where the hypothesis, meaning the sufficient condition, is both sufficient and necessary and the conclusion, meaning the necessary condition, is both necessary and sufficient. Basically these sentences are really just "If then and only if statements in the same sentence.
DeleteSo if someone sees a sentence that reads, "you will be a success in life if and only if you take your father's advice, you would symbolize this sentence as follows: SIL <--> TFA. This mans you have two conditionals in one: 1. if you are a success in life, you took your father's advice. 2. If you take your father's advice, you'll be a success in life.
An easy way to deal with this is to break the sentence down into its component if then statement and only if statement. Then it's clear that the logic is unidirectional.
What about "only accessible to a select group of employees"?
ReplyDeleteI would think to diagram this as: accessible ---> select group of employees.
Could you please explain this? It seems tricky.
Although "only" modifies "select group of employees," it is a sufficient condition indicator in this sentence. To better express my point, let's make the sentence more specific:
Delete"The vault is only accessible to a select group of employees."
Consider these 2 sentences:
1) "If something is accessible, then you are one of a select group of employees."
2) "If you are one of a select group of employees, then something is accessible."
In the 1st sentence, "accessible" could refer to any object/situation and is incorrect.
The 2nd sentence is correct: if you are one of a select group of employees, something is accessible- the vault.
In S--->N reasoning, if a characteristic/action is being attributed to a group/individual, then the relationship always goes:
Group/Individual ---> Characteristic/Action
I love your blogs. They're really instructive and great. I especially love the "way #1" and "way #2," having to do with SC's first/second and NC's second/first. It's a simple thing to see, so long as one has a couple of good examples to keep this in mind. Fir instance, the sentence, "If I hit a glass with a hammer, the glass will break." In that sentence, it is clear that hitting the glass with the hammer (the SC) must happen first, in order that you break the glass with the hammer.
ReplyDeleteConversely, consider the statement, "You don't deserve praise unless you did something deliberately." In that case, the NC, "doing something deliberately," comes before deserving praise because it is the minimum condition that must be met before you can deserve praise; meaning, if you did not do something deliberately (first), then you do not deserve praise. So you would have to have done something deliberately to deserve praise.
As u said, "unless" incidcates necessary condition. What about the sentence "Never know end of TV play unless it made in Korea"?
DeleteDo u means that "made in Korea" must be occured before you can tell "the end of TV play", which meaning, if the TV Play don't made in Korea (first), then you don't know the end.
That looks like a sufficient condition, and it's missing the necessary condition (the "then" statement). What's the rest of the sentence?
ReplyDeleteHi Steve,
ReplyDeleteI'm working through your 4-month study schedule and am having trouble with the word "enables" as it comes up in LR stimuli. i.e) "A enables B..." PrepTest45 S4 #18, or PT46 S2 #7.
Does this "enables" imply that A is sufficient for B to occur, or that A is required/ necessary?
Thank you!!
I could be mistaken, but using a standard dictionary definition of enable, it seems as though "enables" would introduce a necessary condition. I interpret enabling to be synonymous with 'activating' the necessary condition (i.e. makes it possible, but does not guarantee it). See below:
Deleteenable
verb
the brace will enable you to walk more steadily: allow, permit, let, give the means, equip, empower, make able, fit; make possible, facilitate; authorize, entitle, qualify, etc.
Hi! I'm still a bit confused as to why "always" signifies the necessary term? I was under the impression that broad statements signify the sufficient while narrow ones signify the necessary. Is always actually a narrow term?
ReplyDelete