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Ch 13 Formal Logic Additive Inference Drill #3 and #6

mbm269
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Hello, I am not understanding how to attack formal logic questions. Specifically compound statements. I think it is best to identify my concerns and issues by addressing specific problems.

For example:

On page 459 Question 6 -
Some Ns are Os
No Os are Ps
No Ps are Qs
All Qs are Rs

I understand I should start at the N in my diagram, but not sure why or where I stop with the "some train". I feel like on some problems I should stop at arrows pointing in the same direction of the train, but some problems ignore that rule. I guess my main question/concern is: when do I know I should stop when utilizing trains?

For example:

for question 3: although I got this correct, I am unsure why I am allowed to make inferences going backwards from H to E (eg., how do I know I don't stop at F?)

Thanks, I have been having the most difficulty with this sections and I hope I could gain some clarity!
Dave Killoran
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mbm269 wrote:Hello, I am not understanding how to attack formal logic questions. Specifically compound statements. I think it is best to identify my concerns and issues by addressing specific problems.

For example:

On page 459 Question 6 -
Some Ns are Os
No Os are Ps
No Ps are Qs
All Qs are Rs

I understand I should start at the N in my diagram, but not sure why or where I stop with the "some train". I feel like on some problems I should stop at arrows pointing in the same direction of the train, but some problems ignore that rule. I guess my main question/concern is: when do I know I should stop when utilizing trains?


You go as far as you can, then stop! In other words, don't stop until forced to. In the diagram you reference above, the two double-not arrows in a row are a dead end. You cannot jump across them in any fashion, so they are the end of the line regardless of which direction you come at them from. So, in the following diagram I can go from N to P, and then also from R to P:

..... ..... N :some: O :dblline: P :dblline: Q :arrow: R



mbm269 wrote:For example:

for question 3: although I got this correct, I am unsure why I am allowed to make inferences going backwards from H to E (eg., how do I know I don't stop at F?)

Thanks, I have been having the most difficulty with this sections and I hope I could gain some clarity!


Basically because you can make the inference, so you should. In this instance, we know that F :arrow: H, right? so that diagram could alos be:

..... ..... E :dblline: F :arrow: H

That allows for an inference from H back to E, so we make it.

The rule here is to keep going until you can't, but also to recycle in your inferences so as to not miss a connection!

Not easy stuff at first, but it gets much clearer with a little time. One thing that helps is to see other discussions about this specific drill, most of which can be found here: search.php?keywords=additive&fid%5B0%5D=13. Look for the posts I wrote, which will hopefully give you further insights into how this works :-D

Thanks!
Dave Killoran
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