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new formal logic quiz

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new formal logic quiz [#permalink] New post 31 Aug 2003, 04:11
Premises:

(1) A is necessary for B
(2) B, unless C
(3) A is sufficient for D

Which of the following is the correct conclusion?

(1) D, unless A
(2) A, unless D
(3) C, unless D
(4) D, unless C
(5) none of the above
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 [#permalink] New post 31 Aug 2003, 05:07
mmmm...
id say (1) and (2) say the same and so do (3) and (4)... and id say that (1) is wrong and (3) can be true, but can be not true, so i vote for (5)
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 [#permalink] New post 31 Aug 2003, 06:18
Alas, (5) is wrong. I do not see a clear rationale, only telling fortunes by coffee ground. A hint—all the premises have to be transformed into an if/then form.

Last edited by stolyar on 31 Aug 2003, 07:04, edited 1 time in total.
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 [#permalink] New post 31 Aug 2003, 06:40
alas, alas! that is exactly what i tried... let me think:

(P1) A is necessary for B
this means "if not A, then not B"... i visualize this as B<A, where "<" means "contained in"

(P2) B, unless C
this means "if not C, then B"... which equals "if not B, then C"... i visualize this as B and C intersecting each other

(P3) A is sufficient for D
this means "if A then D"... i visualize this as A<D

now...

(Q1) D unless A... this means A can be true while D is false... which is in contradiction with P1

(Q3) C unless D... we can have C true, D false; C true, D true; C true, D false, but not C false and D false... lets see... if not C (C false), by P2, then B... if B, by P1, then A... if A, by P3, then D...

i would now vote for (3) AND (4)... (they are equivalent, arent they?)
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 [#permalink] New post 31 Aug 2003, 06:53
Another hint: transform all the premises in a clear and comfortable form, and unite them:

(1) A is necessary for B== If B, then A
(2) B, unless C ======= If not C, then B
(3) A is sufficient for D == If A, then D

So, we see the chain: (2)—(1)—(3): If not C, then B. If B, then A. If A, then D.

Then, formulate the right conclusion in 2 steps.
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 [#permalink] New post 31 Aug 2003, 07:02
aargh! im feeling so stupid!
we have B=>A, notC=>B, A=>D... or notC=>B=>A=>D

D unless A? notD=>A false (in fact, notD=>notA)
A unless D? notA=>D false
C unless D? notC=>D... winner!!!!
D unless C? notD=>C... id say this is equivalent to notC=>D... so winner as well, isnt it???

i dont get it stolyar, sorry... so ashamed... i still think answer is (3) AND (4)
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 [#permalink] New post 31 Aug 2003, 07:08
If not C, then B. If B, then A. If A, then D.

Step 1: If not C, then D. This equals to...
Step 2: D, unless C.

However, we can transform Step 1: If not D, then C; or C, unless D.

(3) and (4) are the correct answers.

New FLQs coming soon.
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 [#permalink] New post 31 Aug 2003, 07:15
great question, thx!
  [#permalink] 31 Aug 2003, 07:15
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