Formal Logic Questions

thouse
Posts: 75
Joined: Fri Jul 23, 2010 9:46 am

Formal Logic Questions

Postby thouse » Wed Sep 01, 2010 12:30 pm

I was going through the Nova's Master the LSAT book and I have some questions about the formal logic section

1 I>~D
~D
therefore I (but then they say this diagram is the same structure) N > H
H
therefore N

Can someone explain to me why these structures are considered the same??

2. My next question is "No one will be admitted to Yale Law School unless he or she studies hard for the LSAT. No one studied for the hard for the LSAT unless he or she was not a graduate from Tri-State University.

The first diagram is ~SH > ~Y, I thought it should have been ~Y> SH (making the unless phrase the necessary and negating the sufficient)
The next diagram is ~(~G) > ~SH. Now I definitely need help understanding where the double negative comes in but it looks like in this book instead of doing the "Unless" equation they start off with the contrapositive but I could be wrong.Then they say two negatives make a positive so you get G>~SH and using the transitive property or "linkage" you end up with G>~Y

Ok you guys please Help!!! One last question, which logical reasoning question types HAVE to be diagrammed or would be best solved if diagrammed

Audio Technica Guy
Posts: 317
Joined: Tue Jun 29, 2010 5:21 pm

Re: Formal Logic Questions

Postby Audio Technica Guy » Wed Sep 01, 2010 12:44 pm

thouse wrote:I was going through the Nova's Master the LSAT book and I have some questions about the formal logic section

1 I>~D
~D
therefore I (but then they say this diagram is the same structure) N > H
H
therefore N

Can someone explain to me why these structures are considered the same??

2. My next question is "No one will be admitted to Yale Law School unless he or she studies hard for the LSAT. No one studied for the hard for the LSAT unless he or she was not a graduate from Tri-State University.

The first diagram is ~SH > ~Y, I thought it should have been ~Y> SH (making the unless phrase the necessary and negating the sufficient)
The next diagram is ~(~G) > ~SH. Now I definitely need help understanding where the double negative comes in but it looks like in this book instead of doing the "Unless" equation they start off with the contrapositive but I could be wrong.Then they say two negatives make a positive so you get G>~SH and using the transitive property or "linkage" you end up with G>~Y

Ok you guys please Help!!! One last question, which logical reasoning question types HAVE to be diagrammed or would be best solved if diagrammed



I have no idea what you are asking with the first question. The second question is easy enough. With unless, you can think of whatever comes immediately after unless goes on the right side, as it is the required thing. In our case that is "studies hard". The left side takes whatever else there is and negates it. In our case we must negate "no one will be admitted to yale law school" turning it into "if admitted to Yale Law School". This goes on the left.

You get:

if admitted to Yale Law School --> Studied hard

Contrapositive:

If didn't study hard --> Not admitted to Yale Law School.

NYCLSATTutor
Posts: 209
Joined: Sun Jul 11, 2010 2:22 pm

Re: Formal Logic Questions

Postby NYCLSATTutor » Wed Sep 01, 2010 12:46 pm

1.

I-> ~D (if I then not D) and ~D does not equal anything. You can't logically conclude anything from those two statements. That is, assuming that they are both premises.

I suggest you buy a book other than Nova...

thouse
Posts: 75
Joined: Fri Jul 23, 2010 9:46 am

Re: Formal Logic Questions

Postby thouse » Wed Sep 01, 2010 1:08 pm

Question 1.

If he is innocent, then when we hold him under water for sixty seconds he will not drown. Since he did not die when we dunked him in the water, he must be innocent.

Diagram I>~D
~D
therefore I

Then the correct answer choice which asked to find the one that had the similiar logical structure was:

There were nuts in that pie I just ate. There had to be, because when I eat nuts I break out in hives, and I just noticed a blemish on my hand.

Diagra N > H
H
therefore N

what I need to know if what are the structures considered similar??

NYCLSATTutor
Posts: 209
Joined: Sun Jul 11, 2010 2:22 pm

Re: Formal Logic Questions

Postby NYCLSATTutor » Wed Sep 01, 2010 1:25 pm

Ok, I see what you are asking.

First of all, please be aware that the logic structure is the same, but that they are both flawed arguments.

Both structures have two premises. A conditional premise and a premise that is just a fact. In both structures the fact that is stated (~D and H) correspond to the 'then' part of the conditional. In both structures the conclusion is same as the 'if' part of the conditional (I and N).

In fact the only difference is the that in the first question there are negatives involved, and in the second there aren't. But this has no bearing on the structure of the argument as long as they are consistent.

thouse
Posts: 75
Joined: Fri Jul 23, 2010 9:46 am

Re: Formal Logic Questions

Postby thouse » Wed Sep 01, 2010 1:30 pm

Ok now I get so it doesn't have to LOOK the same (meaning they don't both have to have negatives) just the fact that the premises are located in the same part of the stimulus as well as the conclusion.

Which question types do you think have to be diagrammed this way? And then also my question above about the the double negatives.

JesusChrist
Posts: 384
Joined: Wed Aug 25, 2010 12:44 am

Re: Formal Logic Questions

Postby JesusChrist » Wed Sep 01, 2010 4:10 pm

EDIT: I misread, you're right, I think that logic is flawed.

And yeah, the Yale thing is right. Here's what I get:

Y -> SH
SH -> ~G
Infer: Y -> ~G
contrapositive: G -> ~Y

What they're essentially saying is that if you graduated from Tri State University, you weren't smart enough to get into Yale. lol Pretty cheeky for a prep book.

All that they did was use the contrapositive to make it more difficult; so Y > SH becomes ~SH > ~Y.
Lastly, they use double negatives because in formal symbolic logic you're not supposed to remove negations. The reasoning in symbolic logic is that just because there is a double negative doesn't technically change the rule, it just changes how it's expressed. Turning double negatives into positives is just something you do informally.

You got the first diagram wrong because you forgot the negate the segment that precedes the unless. The stimulus says "NO one will be admitted to Yale", so because of the unless that turns into Y.

thouse
Posts: 75
Joined: Fri Jul 23, 2010 9:46 am

Re: Formal Logic Questions

Postby thouse » Thu Sep 02, 2010 8:20 am

But where are they getting the double negative from? What part of that sentence indicates the double negative?

JesusChrist
Posts: 384
Joined: Wed Aug 25, 2010 12:44 am

Re: Formal Logic Questions

Postby JesusChrist » Thu Sep 02, 2010 4:10 pm

thouse wrote:But where are they getting the double negative from? What part of that sentence indicates the double negative?



No one will be admitted to Yale Law School unless he or she studies hard for the LSAT. No one studied for the hard for the LSAT unless he or she was NOT a graduate from Tri-State University.

This gets you SH->~G because you negate the first part, the contrapositive makes it ~~G->~SH, meaning G->~SH




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