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# If A, then B. If B, then C. If C, then D. If all of the

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VP
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If A, then B. If B, then C. If C, then D. If all of the [#permalink]

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19 Apr 2005, 22:34
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If A, then B.
If B, then C.
If C, then D.

If all of the statements above are true, which of the following must also be true?

(A) If D, then A.
(B) If not B, then not C.
(C) If not D, then not A.
(D) If D, then E.
(E) If not A, then not D.

Last edited by MA on 20 Apr 2005, 08:38, edited 2 times in total.
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19 Apr 2005, 23:28
i so want to select D - but i know it is blatantly wrong...

Will pick C - though dont have a good reason.

E and B are in same lines, so choosing one of them seems wrong to me.
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20 Apr 2005, 00:15
C)...

If A, then B.
If B, then C.
If C, then D.

if it rains(A) i take my umbrella(B).
if i take my umbrella(B) i will wear my hat(C).
if i wear my hat(C) i will go and drink a coffee(D).

(A) If D, then A. => i drink coffee when it rains as well when the sun shines and for many other reasons => wrong
(B) If not B, then not C. => when i dont take my umbrella i will wear my hat anyway => wrong
(C) If not D, then not A. => A is a condition for B; B is a condition for C; C is a condition for D. i dont drink a coffee, so the preceeding conditions did not happen. => right
(D) If D, then E. => nothing about E => wrong
(E) If not A, then not D. => i drink my coffee anyway. maybe it rains, mabye it isn`t raining. => wrong
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20 Apr 2005, 00:26
it should be B because C is a necessary condition for B, abd if there is no B then there is no C

regards
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20 Apr 2005, 05:43
vikky267 wrote:
it should be B because C is a necessary condition for B, abd if there is no B then there is no C

regards

If B, then C.

(B) if not B, then not C.

Let's exemplify it.

if it rains, I'll take an umbrella.
can it prove that if it doesn't rain, I do not take an umbrella.
I don't think so.

But we can say if I don't take an umbrella, then it must not rain.

So, I lean to C.
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20 Apr 2005, 06:00
yep "C" shud be it.....

If A, then B.
If B, then C.
If C, then D -----> if not D ---> not C ---> not B ----> not A
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20 Apr 2005, 06:43
(C) Transitive and Contrapositive property.
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20 Apr 2005, 08:38
OA is (C).
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20 Apr 2005, 19:00
If A->B, B->C, C->D

(A) is out. We only know If A->B->C->D. So If A then D, not the other way roudn
(B) is out. We only know if !C, then !B.
(C) is the anwer. !D->!C->!B->!A so If !D then !A
(D) Can't link D to E
(E) From the logic in C, we know !A cannot be logically linked with !D

C it is.
20 Apr 2005, 19:00
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