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Unless Equation - LRB, 2016 Ed., pg. 223 #3

avengingangel
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In questions 3 and 5 on page 223, I would appreciate explanations for the diagrams/meaning of the following conditional statements. I am not understanding how the book is getting the diagrams it is, after applying the Unless Equation.

#3, answer choice (C):
"No athlete can become a champion without a superior mastery of athletic techniques."
The book diagrams this as: champion :arrow: mastery of athletic technique

I am getting: ~champion :arrow: ~mastery of athletic technique ; contrapositive: mastery of athletic technique :arrow: champion. Here's how:

1) Without triggers the Unless Equation
2) What comes after without become the nec. condition, ~mastery of athletic technique (it is negative bc it is modified by the "No" at the beginning of the sentence [I referenced #3 & #12 on pgs. 176 & 177 to confirm that!])
3) The remaining term is negated and becomes the suf. condition, ~champion (I am negating "athlete can become a champion)
4) So.... the diagram is: ~champion :arrow: ~mastery of athletic technique. Right?! I feel like I'm doing everything correctly... no idea how the book is getting champion :arrow: mastery of athletic technique...

Any insight would be so helpful!! Thank you!!!!!
Dave Killoran
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Hi Angel,

Thanks for the questions! I split this one into 2 posts since we like to keep each question separate for searching purposes :-D The other question is now at: viewtopic.php?t=11250.

I think the problem here is that you are mis-applying the Unless Equation. Remember, it works as follows:


    1. Whatever term is modified by “unless,” “except,” “until,” or “without” becomes the necessary condition.
    2. The remaining term is negated and becomes the sufficient condition.

So, how does that apply to answer choice (C)? Let's take a look:


    (C): No athlete can become a champion without a superior mastery of athletic techniques.

Let's start with Step 1, the part modified by "without" becomes the necessary condition:


..... Sufficient Condition :arrow: "a superior mastery of athletic techniques"


Now, Step 2, negate the remainder and make it the sufficient condition. In this case, the "no" gets dropped, leaving:


..... "athlete can become a champion" :arrow: "a superior mastery of athletic techniques"

When reduced, that appears as:


..... Champion :arrow: Superior Mastery

And that is the diagram in the book :-D

What you are doing is trying to shift the "no" to the necessary AND apply the Unless Equation. You can't do both—it's one or the other, not both. When you apply the Unless Equation, just handle the entire sentence as-is. The good thing is that you are covering this now, and not finding it out on the test itself!

The same issue is in play on #5 too.

Please let me know what you think. Thanks!
Dave Killoran
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avengingangel
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Dave, this is really helpful, specifically the part where you say that you cannot apply the No to the Necessary condition AND apply the Unless Equation. Because it does not explicitly say that in the Bible (at least anywhere that I can see, up to this point), I had no reason not to do both things.

Like I mentioned in my original post, I even referenced #3 and #12 on pg. 176 & 177 to confirm the process of applying the "No" at the beginning of the sentence to modify the necessary condition. For example,

#3 - "No robot can think" is properly diagrammed as Robot :arrow: ~Think
#12 - "No citizen can be denied the right to vote" as Citizen :arrow: ~denied right to vote

Thus, that is why I applied the "No" to "superior mastery" in #3 (C) on pg. 223 before I applied the Unless Equation. It was my understanding that that was the proper diagram for the sentence.

So that's really helpful to know that when there is an "Unless"-type of word in the sentence, you do NOT apply the "No" at the beginning of the sentence (if there is one) to the necessary condition. While I'm here, are there any other instances where you do not that??

And thanks for separating out #5 into a different post and explaining that. Makes sense as well.
Nikki Siclunov
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Hi Angel,

Let me add my 2c here. It is imperative to understand the entire sentence at a more general, holistic level before you delve into the specifics of your diagram. There is a world of difference between the following two statements:

    No robot can think.

    vs.

    No robot can think, unless it is programmed to think.

In the first instance, we have Robot :dblline: Think. The two propositions are incompatible with one another. If something can think, it's not a robot; if it is a robot, it cannot think. In the second example, the relationship between being a robot and thinking is more complex: it is conditional upon whether or not the robot has been programmed to think. Thus, if a robot can think, it must be programmed to do so (Robot think :arrow: Programmed to think).

Check out a few blog posts that might be of interest:

Diagramming LSAT Conditional Statements 101: Advantages of The Unless Equation

PowerScore LSAT Forum Post of the Day: Dealing with Negatives (particularly Unless) in Conditional Reasoning

Beyond "Unless": Advanced Conditional Reasoning on the LSAT

Hope this helps a bit! :-)

Thanks,
Nikki Siclunov
PowerScore Test Preparation
Dave Killoran
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avengingangel wrote:Dave, this is really helpful, specifically the part where you say that you cannot apply the No to the Necessary condition AND apply the Unless Equation. Because it does not explicitly say that in the Bible (at least anywhere that I can see, up to this point), I had no reason not to do both things.


Hi Angel,

Let me add one more thing here, which is that indeed I don't explicitly rule out the two things occurring together, but that's because description of the Unless Equation was meant to be all-inclusive. That is the entire technique, and the examples and drills then support that idea. It's more or less impossible to write any book in such a way that you rule out all the possible combination of approaches so the key here is that should you encounter a similar situation (which really isn't all that likely), ask yourself why your diagram is different than that in the book. That will be your first clue that you may have gotten on the wrong path somehow. Fortunately, that's the whole point of studying—you discover these things now, and iron them out before the test itself :-D

Thanks!
Dave Killoran
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avengingangel
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Thank ya for all the help and further explanations!
MeghanV
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Hello,

I am still having difficulties with Question #3 on P 223.
Specifically, I am not understanding why answer A is a Mistaken Reversal.

The diagram is C :arrow: M
If you are a champion, then you must have superior mastery of athletic techniques.

Answer choice A reads:" Only champion athletes have a superior mastery of athletic techniques."

Answer choice A seems like a repeat to me. What part is being reversed?

Thank you!
Adam Tyson
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Your clue that this is a mistaken reversal, MeghanV, is the placement in that answer choice of the word "only", which is of course a necessary condition indicator. Since the "only" is referencing Champions in that sentence, you would diagram answer as:

M :arrow: C

That has being a champion as a necessary condition, not as a sufficient condition as it was in our stimulus.

Our stimulus proves that champions have mastery of athletic techniques, but it could be true that other folks also have that mastery! The necessary condition of mastery can occur even when the sufficient condition of championship does not. So it isn't necessarily true that only champions are masters, even though all champions are masters.

Watch out for those conditional indicator words, such as "only", and diagram them whenever you have any doubt about whether the answer you are looking at is correct or not.

Keep up the hard work!
Adam M. Tyson
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MeghanV
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Hi Adam,
Thank you for the additional explanation--I now see the mistaken reversal.
I haven't thought too much about diagramming the answer choices, but that can help as well!
Thank you!