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General questions relating to the LSAT Logic Games.
 Heather
  • Posts: 11
  • Joined: May 31, 2015
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#18809
Hello.
I am a bit confused about linkage.
I understand most of the basics but I would like to know what the result is of two " :dblline: " combined. For instance, does S :dblline: D :dblline: E mean S :dblline: E?

Furthermore, I know that S :arrow: W :dblline: Y then turns to S :dblline: Y
but what would be the result of S :dblline: W :arrow: Y (the arrow coming AFTER the double not arrow)?
Would it be S :arrow: Y Or S :dblline: Y?

Thank you!
 Jon Denning
PowerScore Staff
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#18810
Hey Heather,

Thanks for the questions and welcome to the Forum! Proper inferences from these types of chains is hugely important, and not just for Games, so I'm glad you're addressing this early on!

The double-not arrow ( :dblline: ) in particular can cause problems for people, but hopefully I can help clear up some confusion.

I'd encourage you for now to think of that double-not as its two component relationships, instead of the single connection. That is, if we have something like this:

..... A :dblline: B

What that really tells us is two things:

..... A :arrow: NOT B ; and B :arrow: NOT A

In other words they can never be grouped/selected together, so the presence of one rules out the other. But when you treat the original diagram as two parts, it becomes much easier to see how chains can and can't be formed. Consider two new rules we could add to the diagram(s) above:

..... C :arrow: A

..... B :arrow: D

What inferences might result from the addition of those new ideas? Well, we can tie C to A as follows:

..... C :arrow: A :arrow: NOT B

..... So C :arrow: NOT B

Since the arrows all go in the same direction an inference is possible! But what about the B and D rule we added? To connect it, we need it to be linked via positive (without the "NOT") B:

..... D <--- B :arrow: NOT A [sorry, there's no right-to-left arrow icon]

But in looking at that the arrows go in different directions, so unfortunately we can't make any absolute inferences about D and A. That's something the test makers love to use as a trap, so you have to be really careful!

That's also why C :arrow: A :dblline: B allows for an inference (C :dblline: B), while A :dblline: B :arrow: D does not: the "B" in that connection isn't a positive B when moving from A (A gives you NOT B), but it is a positive B going to D...so you don't actually have the same variable there to make the connection in the first place!

By treating those types of relationships individually (rather than combining with :dblline: ) you'll save yourself from making mistakes as you get more comfortable. And with time and practice you can begin to use double-nots more frequently once you're completely confident.

I hope that helps!
 Heather
  • Posts: 11
  • Joined: May 31, 2015
|
#18821
Hi Jon!

Thanks for welcoming me and thank you for the response. It helps clarify a few points, I do however want to know what the scenario would be if a negative sufficient condition were present in the question,
For instance if a rule states :A :arrow: NOT B (and by way of its contrapositive B :arrow: NOT A)
and a second rule states NOT B :arrow: P

We can now form the chain (without using double not arrows to make it simpler for me)
A :arrow: NOT B :arrow: P
and in this turn would equal to A :arrow: P (while of course, keeping in mind that B and P can still occur together)

I just want to know whether in the negative sufficient condition present above we can equate
A :arrow: P as correct.
And also- just to reiterate once again, according to your explanation if a negative variable is present in the middle of a chain (A :dblline: B :arrow: P) A :arrow: P is NOT possible unless the question specifically states that when B is not chosen (NOT B) then P is chosen - Correct?
 Jon Denning
PowerScore Staff
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#18825
Hey Heather,

That's exactly right! Any time you have the same term (positive or negative) and you can use it to connect pieces so the arrows all point in the same direction, then you can make inferences all the way down the chain!

I'm also really happy to see you note with NOT B :arrow: P that B and P can still occur together. That's a very important idea and one that a lot of people fail to see, so well done! All we know there is that they can't both be absent--one gone forces the other in--and nothing about what happens when one or the other (or both) is/are present.

And you're correct on your second question/point, too! The problem is that the double-not makes it seem like positive "B" is the shared variable, when in reality the double-not gives you a "NOT B." And you can't connect with a "B" and a "NOT B," since they aren't the exact same term.

Nice work!

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