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# English Logic

Author Message
Intern
Joined: 20 Sep 2008
Posts: 45

Kudos [?]: 13 [0], given: 0

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20 Sep 2008, 23:28
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.

I have chosen E however, the right answer is C? i would appreciate it if someone could help to clarify it?

Kudos [?]: 13 [0], given: 0

Intern
Joined: 20 Sep 2008
Posts: 7

Kudos [?]: 2 [0], given: 0

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21 Sep 2008, 01:50
A - A => D, but not D => A
B - B => C, but not ~B => ~C
D - there is no E in the context
E - A => D, but not ~A => ~D

C - D can come only if C comes. So, ~D => ~C => ~B => ~A.

My choice - C.

Kudos [?]: 2 [0], given: 0

VP
Joined: 05 Jul 2008
Posts: 1402

Kudos [?]: 437 [0], given: 1

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21 Sep 2008, 14:10
jugolo1 wrote:
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.

I have chosen E however, the right answer is C? i would appreciate it if someone could help to clarify it?

A -> B and contrapositive is ~B -> ~A

B->C ~C -> ~B

C -> D ~D -> ~C

Apply transitivity on all the contrapositives and you will arrive at C

Kudos [?]: 437 [0], given: 1

Re: English Logic   [#permalink] 21 Sep 2008, 14:10
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