PS LR Bible: Please clarify the aspect of formal logic

obsrvr
Posts: 7
Joined: Sun Mar 17, 2013 11:04 pm

PS LR Bible: Please clarify the aspect of formal logic

Postby obsrvr » Wed Mar 20, 2013 11:43 am

I am going through the PS LR Bible and I have the question regarding the logic behind the following statement.

A few of these houses do not meet city architectural codes. None of the houses that meet city architectural codes are big.

So I am diagramming according to what was learned:

H some ~MCAC --> B , where H - houses, MCAC - meet architectural codes, B - big.
So according to the book one of the proper inferences would be H some B, or some of the houses are big, or must be big. My diagram: H some B.

For the sake of completeness, in the Some Train Diagramming Drill page (abstract example): D some ~E --> F, then proper inference: D some F (correct me If I am wrong, but I feel my slightly altered example equivalent to precise version from the book). In this case Some Ds are not Es and No Es are Fs. Just because Some Ds are not Es and No Es are Fs, I do not think I can for sure say that some Ds must be Fs (which is correct inference as per the book).

Now, I am completely thrown off by these inferences. With the former example, I feel that if some houses do not meet architectural codes, then it is not necessarily true that they, or least one of the houses must be big. I think it is possible that some of the houses are big (based on the info above), but it does not have to be the case. I mean, the house that do not meet architectural standards can sort of exist on its own, no? Perhaps, it would be good to see the diagram of the sets [Venn diagram].

On the other hand, I cannot find a correction relating to the issue I am grappled with, so the book must be correct.

Perhaps I missed something in the book regarding the LSAT universe, but l feel logically it does not make sense, just because things connected they do not have to be a part of another, I reckon. Please tell me where I am wrong in my thinking and what I might be missing.

Also, in case the post is within inappropriate location, please let me know of the best place to ask similar "technical" questions.

Thanks for help.

Cambridge LSAT
Posts: 270
Joined: Mon Aug 24, 2009 3:26 pm

Re: PS LR Bible: Please clarify the aspect of formal logic

Postby Cambridge LSAT » Wed Mar 20, 2013 12:30 pm

obsrvr wrote:None of the houses that meet city architectural codes are big.

You have reversed the direction of the arrow for this part. In if/then form, it would read "If a house meets architectural codes, then it is not big." So, diagramming the statement yields the following:
MCAC → ~B

The contrapositive is B → ~MCAC. Since ~MCAC is not the sufficient condition of either the original or its contrapositive, we can't infer anything if we know that a house doesn't meet city architectural codes.

obsrvr
Posts: 7
Joined: Sun Mar 17, 2013 11:04 pm

Re: PS LR Bible: Please clarify the aspect of formal logic

Postby obsrvr » Wed Mar 20, 2013 12:56 pm

Cambridge LSAT wrote:
obsrvr wrote:None of the houses that meet city architectural codes are big.

You have reversed the direction of the arrow for this part. In if/then form, it would read "If a house meets architectural codes, then it is not big." So, diagramming the statement yields the following:
MCAC → ~B


Cambridge LSAT wrote:
obsrvr wrote:None of the houses that meet city architectural codes are big.

You have reversed the direction of the arrow for this part. In if/then form, it would read "If a house meets architectural codes, then it is not big." So, diagramming the statement yields the following:
MCAC → ~B


Thanks for pointing it out! Perhaps, we can rephrase the sentence to:

A few of these houses do not meet city architectural codes. All of the houses that do not meet city architectural codes are big.

Then it makes sense, I guess.

Correct me if my rephrasing is incorrect.

I guess the mistake was that I was drawing the parallel between D some ~E --> F and the above incorrectly.




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