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English Logic

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Intern
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English Logic [#permalink]

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New post 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?
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Re: English Logic [#permalink]

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New post 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.
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Re: English Logic [#permalink]

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

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