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#113336 - 10/11/03 12:38 PM Re: Logic problem  
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was the error?

and or, no?



formerly known as etaoin...
#113337 - 10/12/03 12:37 AM Re: Logic problem  
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I've just read the top few posts--and the problem appeared to be poorly worded. However, based one the wording, only one statement appeared to be true. Still, I had the same problem with the wording that Faldage and AnnaS did. And someone way up there suggested and/or instead, which would have clarified the problem. The capitalization in the problem was off, too.

AnnaS: I teach at a magnet school, but it's not for any of the scienes; it's the magnet school for the fine and performing arts where logic ain't necessarily so.


#113338 - 10/12/03 11:23 AM Re: Logic problem  
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what's a magnet school?


#113339 - 10/12/03 01:40 PM Re: Logic problem  
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A magnet school is a school that attracts students that aren't anemic.


#113340 - 10/12/03 04:08 PM Re: Logic problem  
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that's a Sominex®, Fald...



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#113341 - 10/13/03 01:15 PM Contradiction not clarification  
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In this particular case, the author clarifies the response with the second sentence.

With respect, the author does not "clarify" the response with the 2nd sentence, the author contadicts it.

Here are the sentences:

"All Seniors at The Academy take calculus and physics.
Some seniors take both courses."

The phrase "Calculus and physics" is not equivalent to "calculus or physics".

The 2nd sentence here contradicts the 1st, and the reader does not have sufficient information inside the 4 corners of the "logical problem" to decide which sentence should prevail.

It is simply arbitrary to say the 2nd sentence should prevail over the 1st. Why not the 1st over the 2nd?

In this situation, the only logical thing to do is to answer "None of the above" and ask for more information to resolve the apparent contradiction.

Since there is no "None of the above" option, one should 'think outside the box' and provide the correct answer [literally outside the box] in writing.

Of course, this is a very good lesson for real life.

How many times do we assume something from incomplete or inconsistent input, and end up running off in the wrong direction, wasting time or money, our own or someone else's?

Getting the facts straight in the beginning is the real lesson to be learned from this particular "logic problem". That and having the courage and self-confidence to resist the stampede to the 'wrong' answer simply because it is the best of all the 'wrong' answers provided.

Congratulations to the authors of this problem!

[I just hope the computers which are programmed to tabulate test results will recognize the correct answer scribbled outside the box. Otherwise, we will be punishing, and, worse, extirpating the courage and creativity of our most gifted test-takers.]


#113342 - 10/13/03 06:48 PM Re: Contradiction not clarification  
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How many times do we assume something from incomplete or inconsistent input, and end up running off in the wrong direction,...

- and -

I just hope the computers which are programmed to tabulate test results will recognize the correct answer scribbled outside the box.

You've proved your point nicely... and I agree with the rest of *it, as well.

Sometimes the devil's advocate just ain't taken seriously enough.


#113343 - 10/14/03 01:16 PM Re: Logic problem  
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d. is the standard exclusive OR (XOR)



You are in error, here. And I was in error when I said it was correct. Equivalence is the negation of exclusive or.



k



#113344 - 10/14/03 01:24 PM Re: Contradiction not clarification  
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"Clarifies" was the wrong choice of word.

The first sentence says that all students take both classes. The second says that some students take both classes. If all students take both classes, then it is also true that some students take both classes. Therefore, the second sentence does not contradict the first sentence, but is contained in it AS IT IS CURRENTLY WORDED.

HOWEVER, if the problem had been worded correctly, " ... students take calculus OR physics" THEN the second sentence WOULD HAVE clarified that the OR was intended to be an inclusive OR (just in case the student had any doubt).

I agree with your point, though. All real learning takes place inside a student's head. When students understand something, they have an obligation to themselves to speak up, to have it explained to them. If they do not like the explanation, they should be able to say, "I have no choice but to acquiesce to your answer, but I don't agree with it."

k



#113345 - 10/14/03 01:38 PM Re: Logic problem  
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FF, what precisely was the error?



The error is, as Faldage pointed out, with the use of AND in the first sentence. It should be an OR. In casual conversation, one can use words as one pleases. The criterion of correctness is whether the recipient of the sentence understands it. But in logic problems, some words have very specific meanings, AND being one of them. If you say "P and Q," that means both.

Now we could argue that the student should know what was meant. It then becomes a problem of linguistic interpretation and not a problem about about logical reasoning.

(Back when I took AI, one of the more challenging exercises we had was to take a list of sentences in common English, convert them to statements in the predicate calculus, then reword them to say what the author really meant and convert THOSE to predicate calculus. I know it sounds trivial, but it took a lot of effort to do this.)

k




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