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Conditionality - Need expert thought

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by voodoo_child » Wed Jul 11, 2012 12:08 pm
"Only girls with blue eyes are considered beautiful."

How can I diagram this statement? Thoughts?

I believe that possessing blue eyes is a sufficient condition. Hence, blue eyes -> beautiful. Am I correct?
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by Kasia@EconomistGMAT » Wed Jul 11, 2012 1:35 pm
This is a similar statement to "Only doctors are perceived as smart."
In this case the sentence defines a quality necessary for a condition to be fulfilled.
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by voodoo_child » Wed Jul 11, 2012 2:54 pm
Kasia,
I am not sure what that means. But can you please reply in terms of diagram so that the picture is clear?
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by voodoo_child » Thu Jul 12, 2012 7:08 am
Can any of the experts help me? HELP!!!
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by Bill@VeritasPrep » Thu Jul 12, 2012 7:34 pm
Your arrow diagram is backwards.

Blue eyes ---> Beautiful means that if you have blue eyes, you are considered beautiful. However, the original sentence does not say that blue eyes are sufficient to be considered beautiful. I would diagram it as:

Beautiful ---> Blue eyes. If you are considered beautiful, then you must have blue eyes.

For Kasia's example:

"Only doctors are perceived as smart." This does not mean that being a doctor is sufficient for being considered smart. The diagram would be:

Smart ---> Doctor. If you are perceived as smart, you must be a doctor.

In general, the relationship is:

Sufficient ---> Necessary
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by David@VeritasPrep » Mon Jul 16, 2012 1:12 pm
Bill is exactly right. The "only" goes with the necessary condition.

Was there a specific GMAT question that prompted you to look at formal logic?
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by voodoo_child » Tue Jul 17, 2012 9:15 am
Thanks Bill and David. I have memorized this structure. I recently came across an LSAT CR question that dealt with "only." I was lost with Nec/Suff question. Now, the question makes sense.


thanks for your help.
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by shekhar.kataria » Tue Jul 17, 2012 10:56 am
Hi Bill

I have a Question here

You said
Beautiful ---> Blue eyes. If you are considered beautiful, then you must have blue eyes.
Doubt :- Why cant it be Beautiful ---> A girl with a Blue eye.

IS it because there can be any other group and also there may not have blue eyes but are still considered beautiful.

Please confirm.
Bill@VeritasPrep wrote:Your arrow diagram is backwards.

Blue eyes ---> Beautiful means that if you have blue eyes, you are considered beautiful. However, the original sentence does not say that blue eyes are sufficient to be considered beautiful. I would diagram it as:

Beautiful ---> Blue eyes. If you are considered beautiful, then you must have blue eyes.

For Kasia's example:

"Only doctors are perceived as smart." This does not mean that being a doctor is sufficient for being considered smart. The diagram would be:

Smart ---> Doctor. If you are perceived as smart, you must be a doctor.

In general, the relationship is:

Sufficient ---> Necessary
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by 7777 » Fri Aug 24, 2012 9:51 pm
voodoo_child wrote:"Only girls with blue eyes are considered beautiful."

How can I diagram this statement? Thoughts?

I believe that possessing blue eyes is a sufficient condition. Hence, blue eyes -> beautiful. Am I correct?
sufficient necessary
beautiful>>blue eyes

1 st correct inference==if a girl is beautiful she must be having blue eyes.
2nd correct inference== if a girl doesnt have blue eyes she wont be considered beautiful.


1 st wrong inference==if a girl has blue eyes, she will be considered beautiful.
2nd wrong inference== if a girl is not considered beautiful she doesnt have blue eyes.
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