For problems 3, 9, and 12, I am having trouble understanding why "no" and "only way" modify phrases that are far away from them. I also don't know how to determine which phrase is the sufficient condition and which phrase is the necessary condition for problems 3 and 12 since there aren't any indicators present.
Can you please clarify?
Conditional Reasoning Diagramming Drill, P176, #3, 9, and 12
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Great questions! I think what is tripping you up here is paying too much attention to buzz words and not enough attention to the actual meaning. You always want to be asking yourself, "What is this sentence actually saying?" See if you can re-write the sentence to mean the exact same thing, but be in If-Then format. For example, for number 3, that would be, "If it is a robot, then it cannot think," or "If it can think, then it is not a robot." Then, check that against the original sentence, and ask yourself if it still has the same meaning. That may help with your problem with "no" and "only way," because it will help you step away from worrying about where in the sentence particular words are and instead focus on what those words actually do in the sentence.
A lot of times, looking for indicators will be a great shortcut and will help you out. However, you can't become overly reliant on them, because then you'll come across problems - like 3 and 12 - with no indicator words. For those, you really need to take a step back and think about what the sentence is saying and how each part functions. I'm actually less concerned for these types of questions which term you put first and which you put second; instead, I'm concerned that you correctly diagram it, regardless of which you use as sufficient and which you use as necessary. If your diagram matched either of the diagrams in the answer section, then you understood the relationship and had it figured out, regardless of whether you did the original reasoning or the contrapositive.
I hope that helps!
Thanks for the questions!
Let's start with the idea of "distance." It actually doesn't mean a whole lot; what is more important is which terms modify which elements. That's the key, and in some cases words modify the word right after it, and in other cases they modify ideas far away. You mentioned "only way," and that is a great example of an idea modifying something that is often physically far away in the sentence, so let's start there. That phrase is involved in #9 in the Drill, and since I've discussed that problem previously, I will refer you to two of my discussions of that one: viewtopic.php?t=7708&p=19894 (you get a bonus discussion of #8 there too!) and viewtopic.php?t=4564&p=12004. The key in that one is to understand that "way" refers to an idea that is not introduced in the sentence until a bit later. That's not uncommon in English, and so it happens on the LSAT as well. It's also one of the main reasons that preparing for the LSAT is so valuable, because you get to see situations like this before the actual test, and you can get a complete handle on them before it counts. So, take a look at my post there, and then let me know if that helps clear up the idea with "only way." If not, there's more we can discuss
Drill items #3 and #12 are obviously quite similar, and so we can discuss those together. Each is in the form of "No Xs are Ys." This is irritating at first because the "no" is immediately next to the X, and so your first reaction is to think that the "not" should be on the X. But then when you look at the answer key, you see that that's not the case!
The form of this rule is quite common—especially on Logic Games—so it is good that you are coming up against it now. The way it works is that when you have "No Xs are Ys," the actual negative generated by the "no" ends up being physically on not X, but Y. This is because the "No" applies to all of the elements in X. In other words, if you are in the group X, then we know you don't do something (in this case, you don't do Y). So, it's not that X is negated but that the activity that X would engage in is negated. That's pretty abstract, so let's rephrase that abstract form into something more easily understood. Consider this example:
"No high school senior is attending class tomorrow"
So, when you look at that, what do you know about high school seniors? Well, that none of them will be attending class tomorrow. In other words, if you are a high school seniors, then you will not attend class tomorrow. So, the "no" is something that the high school seniors don't do. This happens because the phrase "no high school seniors" tells you that none of the elements in that group of seniors will do something (attend class), and thus the actual negative symbol is applied not directly to high schools seniors (the group that matches X), but to "attending class tomorrow" (the Y portion):
If the "no" was to be applied directly to "high school seniors" ( HS ACT ), then it would need to be phrased along the lines of, "If you are not a high school senior..."
When we take that analysis and apply it back to a problem like #3, for example, we get:
No robot can think.
That would mean that all elements in the group "robots" do not "think", which would be:
So, take a moment to consider how a phrase like "No Xs are Ys" differs from "If you are not an X, then you are a Y." As you do that, consider also how "No X" is an absolute statement—it means that every X does not have a certain characteristic. Conditional statements, and thus conditional indicators, are often absolute in nature (all, every, none, never, no, etc). That will hopefully help you when you encounter other scenarios you might not have seen before.
Please let me know if that helps. Thanks!
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Yes, this helps a lot. Thank you!
When I answered both problems 3 and 12, I created the contrapositive as your positive. In other words, for #3:
"No robot can think."
I created the positive as: T ---> -R
I created the contapositve as: R ---> -T
The Answer Key gave the positive as: R ---> -T and the Contrapositive as T ---> -R.
I'm not sure that my answer was necessarily incorrect but do understand that I didn't get the positive form. For me, it's easier to use the "no" as an indicator of the necessary condition and to express the necessary condition as a negative. So for question #12:
Positive: RTV ---> -C
Contrapositive: C ---> -RTV
Will this structure lead down an unsuccessful path?
The important thing is to understand the concept. In your case, you're mislabeling the positive and the contrapositive, but you still got it right. That's because you are correctly identifying the relationships created by the problem. What you call them has no impact those relationships and thus no impact on whether you get the question correct.
I don't think it matters what you call each relationship. However, you need to be certain you truly understand the concept of getting the positive and contrapositive and that you are truly getting the correct relationship.
#12 has the answer as C DRV
Instead of using DRV (Denied the right to vote), I viewed the situation as a double negative ("no" and "denied") and turned it into a positive using RV. Thus having:
C RV and the Contrapositive RV C
Is that totally wrong? Am I completely off, did I miss something major?
Hey there Michael, I think your approach is completely valid in this case. If you are not denied the right to vote, then you have the right to vote - I can't think of a third alternative here. That's what we sometimes call a two-value system - there are only two choices, so you either have one or you have the other. If there was a third alternative - someone who is not denied the right to vote but also doesn't have that right - then you would want to do it the way we have it in the explanation. Here, though, your converting the double negative into a positive looks like a winner to me! Good job!
Adam M. Tyson
PowerScore LSAT, GRE, ACT and SAT Instructor
Follow me on Twitter at https://twitter.com/66adamt
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