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, until
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):
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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).
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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 successfully 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 December 2009 LSAT, so I'll tell you right now - that sentence was a joke. I wouldn't be caught dead in a place called "Newtown.")
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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?
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.
ReplyDelete