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logical proposition

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surat
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logical proposition [#permalink] New post   15 Aug 2003, 05:56
hi guys

i don't know how you express it in english, but translated directly from russian it sounds like 'logical proposition problems' :roll: .

here is an example:

we have four students: 1, 2, 3, 4. determine how many of students passed the exam, if it is known that:
1. if 1 passed, then 2 also passed
2. if 2 passed, then 3 also passed or 1 failed
3. if 4 failed, then 1 passed and 3 failed
4. if 4 passed, then 1 passed.

first i wanted to think about this problem in terms of combination or permutation :? , but i am sure it has its own ways of solution.

regards



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Re: logical proposition [#permalink] New post   15 Aug 2003, 06:09
LSAT? :stupid
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Re: logical proposition [#permalink] New post   15 Aug 2003, 06:10
They all Passed

Look at items 3 and 4.
#3. if 4 failed, then 1 passed and 3 failed
#4. if 4 passed, then 1 passed.

No matter what happens to 4, 1 passes, so 1 must pass...so lets start there.

Ok, so looking at item 1, #1. if 1 passed, then 2 also passed.

So now we know that both 1 and 2 passed.

Now, #2. if 2 passed, then 3 also passed or 1 failed. Well, we know 1 can't fail, so student 3 must pass as well.

Now #3 cannot result in student 4 failing, because that would require student 3 to fail, so student 4 must pass as well.
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Re: logical proposition [#permalink] New post   19 Aug 2003, 21:17
mciatto wrote:
They all Passed
Look at items 3 and 4.
#3. if 4 failed, then 1 passed and 3 failed
#4. if 4 passed, then 1 passed.
No matter what happens to 4, 1 passes, so 1 must pass...so lets start there.
Ok, so looking at item 1, #1. if 1 passed, then 2 also passed.
So now we know that both 1 and 2 passed.
Now, #2. if 2 passed, then 3 also passed or 1 failed. Well, we know 1 can't fail, so student 3 must pass as well.
Now #3 cannot result in student 4 failing, because that would require student 3 to fail, so student 4 must pass as well.


great job, mciatto. after your explanation - it is very easy to understand. :)



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Re: logical proposition [#permalink]
19 Aug 2003, 21:17
Moderator:
yashikaaggarwal
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3137 posts

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