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November 13, 2009

LSAT Words: "Except" "unless" "until" and "without" mean...

LSAT Blog Words Except Unless Until Without MeanUPDATE: Also see this newer post: LSAT Numbers: All, Most, Several, Many, Some, None

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I talked about Sufficient and Necessary Condition indicator words a few weeks ago.

However, I left out a couple of important words (except, unless, until, and without) that factor into conditional reasoning.

These special words don't *quite* fit the mold that the others do, so I decided to give them their own blog post.

The words "except," "unless," "until," and "without" frequently appear in the Logical Reasoning section of the LSAT. Their presence often trips up test-takers who have difficulty deciding whether to associate them with the sufficient condition or the necessary condition. The truth is that these words don't neatly fall within either category. The condition with which you associate them should depend upon your approach to translating them.

This blog post will cover two common methods that test-takers can use to correctly translate statements containing these words.

Note: I'm not a fan of Method #1, so just skip to Method #2 if you're not interested in the nitty-gritty.


Method #1: Replace these words with the phrase "If not." This means that you're taking these words to represent the negation of the sufficient condition.

In other words, you're negating whatever immediately follows the words "except," "unless," "until," and "without" and turning that thing, when negated, into the sufficient condition.


The phrase "Not B unless A" would become "Not B if not A." Rearranged in the traditional "If-then" form (sufficient ---> necessary), this would be "If not A, not B."

Diagrammed: Not A ---> Not B

Contrapositive: B ---> A



Example of Method #1 with words replacing variables:

It's not Thanksgiving (B) unless there's turkey (A). (I know it's not Thanksgiving for a few weeks, but I'm hungry for turkey and stuffing now.)

With "if not" replacing "unless":

It's not Thanksgiving if there's no turkey.


Diagrammed: No turkey ---> Not Thanksgiving.

Contrapositive: Thanksgiving ---> turkey.


I'm not a huge fan of this method. Although it seems to be an incredibly simple technique for dealing with these annoying words, it often requires additional steps that Method #2 (below) doesn't.


Remember how we rearranged the order from "Not B if not A" to "If Not A, then Not B" so that the sufficient condition would be in front? Then, we had to take the contrapositive because dealing with a conditional statement involving two negative statements.

Without taking the contrapositive, this method turns "No X unless Y" into "Not Y ---> Not X." We then have to take the contrapositive to create "X ---> Y."


Method #2: Take any of the annoying words ("except," "unless," "until," and "without") as introducing the necessary condition. In other words, whatever immediately follows one of these words is your necessary condition.

Then, whatever other clause is present in the conditional statement will, when negated, become your sufficient condition.


The phrase "Not B unless A" would first become "Not B then A." However, we're not done yet - we still have to negate "Not B" to become "B."

So we have B ---> A. No need to take the contrapositive or rearrange anything.


Example of Method #2 with words replacing variables:

"It's not Thanksgiving (B) unless there's turkey (A)." would first become:

"Not Thanksgiving ---> there's turkey" BUT

we still have to negate "Not Thanksgiving" to become "Thanksgiving."

This gives us "Thanksgiving ---> turkey."

(Meaning that we've directly turned "No X unless Y" into "X ---> Y")

Note: Of course, the sentences containing these words don't always follow the "negative variable - annoying word - positive variable" (No X unless Y) format (or the identical "unless Y, no X" format), so Method #2 isn't always incredibly superior to Method #1. However, I find that Method #2 more frequently gives you a positive and useful conditional statement than Method #1 does.

Keeping the variables positive is especially important when forming long conditional chains. See PrepTest 30 (December 1999), Section 2, Question 18 (page 59 in Next 10) for an example.

Photo by zawtowers / CC BY-NC-ND 2.0



24 comments:

  1. This was a useful tip. Thanks!

    ReplyDelete
  2. Moreover, the PT 30, II, Question 18 was a perfect example for this. Lacking understanding of how to handle the "unless" rule would turn this into a time-consuming question (and one that would likely prompt an incorrect answer choice). Armed with this understanding though, the correct answer can be quickly ascertained.

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  3. Great post, these can be very misleading words on the LSAT. I like the information that you provide here, you are very thorough and provide some great articles; so thanks for that.

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  4. Does this method (at least Method #1) apply to "unless" statements that are NOT double negatives?
    Example:I am golfing today unless it rains.

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  5. Nice post!
    But, how am I suppose to apply these two methods with two positive variables joined by "unless".
    For example: A unless B

    ReplyDelete
  6. @ last post:

    If not A then B

    ReplyDelete
  7. Steve,
    What is the logical structure of a conditional statement that uses "even if"?

    Does "P even if Q" translate to both "Q -> P" and "~Q -> P"? Does it just state that whether Q is true or false has no bearing on P? Are neither Q nor ~Q sufficient for P?

    Thanks,

    Ryan

    ReplyDelete
  8. Great question.

    Answer: it just states that Q does not prevent P from occurring. "Even if" is not by itself an indicator of a conditional statement.

    ReplyDelete
  9. Both methods make me want to stab sharp pencils in my brain.

    I'd do it, but I'm saving my last 4 pencils for the test Saturday and I'm afraid my occipital lobe might dull the lead.

    I don't want to prematurely mash the "easy" button, but can't you just say it's the opposite?

    "It's not Thanksgiving unless there is turkey."

    =

    If it's Thanksgiving, then there's turkey.

    "there will not be a good play unless there are democratic listeners in the audience"

    =

    If there's a good play then there are democratic listeners in the audience.


    Yeah, that works.

    All those rules and methods make me cross-eyed. I see how they work though!

    Caleb out.

    ReplyDelete
  10. Wow! thank you...method 2 is incredibly easier. This info was extremely helpful!

    ReplyDelete
  11. hi
    if you see this, please comment to me about 'unless'=except.

    i'm from S.Korea and i have studied English.
    and I have a question about

    If it were not for A=but for A=except for A=unless for A

    is that right? I mean,
    [but for A=except for A] is correct?
    My teacher've said that is correct.

    but I don't understand!
    please help me..

    ReplyDelete
    Replies
    1. @다르씨:

      "But for" can correctly be understood as meaning "if it were not for" or "except for" (E.g. "But for/except for/if it were not for the LSAT tomorrow, I would attend the party.")

      Now, don't worry about not understanding the usage intuitively, because "but for" used in this way is idiomatic.

      An idiom (in this sense) is defined as
      "an expression whose meaning is not predictable from the usual meanings of its constituent elements...or from the general grammatical rules of a language." (http://dictionary.reference.com/browse/idiom)

      Also, "unless for A" doesn't approximate the meaning of "except for/but for/if it were not for", as used above, and is not correct.

      Delete
  12. Hi:

    I am wondering about another element in these problems. So if the premise is "No A without B or C," how should I translate this? Does it mean I need both B and C together as the necessary condition? Or just either B or C is enough?
    Does it make any differences if it is "No A without B AND C"? Daily English clouded my judgement. Help!

    ReplyDelete
    Replies
    1. Someone correct me if I am wrong.

      But I would translate No A without B or C as If A, then B or C.

      "Or" versus "And" does make a difference. In this example, when A occurs, then either B or C can occur. It's not necessary for both to occur at the same time when A happens. It could happen that B and C can occur together, however, it's not necessary based off of this rule alone. Another rule could bring about that possible occurrence

      No A without B and C would translate to If A, then B and C. That would mean If A occurs, then BOTH B and C have to occur at the same time.

      I hope this helps.

      Delete
  13. Hello! Thank you for the wonderful explanation. I have found it very helpful in my study of LSAT formal logic. I only have one question about the two methods. Is it possible for both methods applied to the same statement to give different conditional statements?

    For example how would you diagram the conclusion of something like Question 19 from PT 57, S2? Or stated in semi-similar terms: "So our bookclub will not retain its ranking unless it increases its funding."

    Using method 2 I get: R --> F
    Using method 1 I get: ~F-->~R

    I am just very, very confused. I think I may be using the 2nd method incorrectly but it has worked for every other statement but the one in this question. Please help if possible!! Thank you!

    ReplyDelete
  14. I think you're switching sufficient versus necessary conditions. It should be R --> F. Remember that anything after the annoying word is the necessary condition and anything before it (and negated) becomes the sufficient. Your example translates as In order to retain its ranking, the book club should increase funding.

    ReplyDelete
    Replies
    1. Hello Christine. Thank you for the quick reply. I am still lost however. I don't understand how the two methods produce two different conditional statements. Should they not be the same statement?

      "So our bookclub will not retain its ranking unless it increases its funding" = R --> F
      But when I use the first method and turn the statement into: "So our book club will not retain its ranking if it does not increase it's funding" = ~F --> ~R which is the contrapositive of method 1's statement. I thought both methods would yield the same statement?

      I'm very sorry to nitpick; I just really want to understand this. Thank you again for your help!!

      Delete
  15. Both answers are correct. They're just contrapositives of each other.

    Method 1:~F-->~R
    Contrapositive:R-->F

    Method 2:R-->F
    Contrapositive:~F-->~R


    Method 2 is superior probably because it's easier to read as statement versus method 1 which is a double negative. But they both say the same thing.

    ReplyDelete
    Replies
    1. Oh Ok. Thank you so much Christine!! Thank you!

      Delete
  16. Seems like method 2 uses the bible method.
    I thought I had a nice grasp of it till I went over some drills and the workbook.
    Could someone kindly help me out with the following questions?

    From the workbook(page 17)
    You cannot enter unless you pay admission
    --> if you do not pay admission, you can enter

    From the bible drill(page 271, A negation drill)
    Unless the stock market rebounds, the economy will not recover this year.
    -> THe economy will not recover this year even if the stock market does not rebound.

    ReplyDelete
  17. Those are the answers on the book

    ReplyDelete
  18. So looking at the second example, it's just showing you how to negate the phrase, which is correct. I think you're confusing what negation test does( only deals with necessary assumption questions) and how to better understand "except", "unless" and "until" arguments. I would suggest reading up on negating on Steve's blog.

    For the second example if we were to truly use the second method. The phrase would read "If the economy recovers this year, then the stock market rebounds.

    ReplyDelete
  19. What about " no one want to fail" how this sentense works?

    ReplyDelete
  20. Sufficient condition indicator also include followings, "To be/In order to" "Will/Will not" "All/Every/Any" "People who"
    Could u please give some examples about those words? Thank you so much

    ReplyDelete