Re: logic questions(pls give full solution)

Posted by Amit Goyal on May 03, 2009; 3:18am
URL: http://discussion-forum.276.s1.nabble.com/logic-questions-pls-give-full-solution-tp2763642p2773470.html

one of a b c and d has committed a crime with the help of another one of them. here are the statements by the four individuals . the statements of the criminal and his accomplice are false and and those of the remaining two are true.
A: if b is guilty of something , then c must be innocent .
B; if a is innocent then c must be guilty
C; if b was the killer then b must have had nothing to do with crime
D: i am innocent

which of the four is the criminal and who is his accomplice?

Solution
 The simplest way could be to consider all six cases one by one and eliminate wrong ones one by one till you find the correct one:
i) A and B are innocent--> C and D are lying, C is lying implies B was killer and D is his accomplice, contradicting B is innocent
ii)A and C are innocent--> B and D are lying, B is lying implies A and C are innocent, that's fine, D is lying implies he is not innocent, that is fine too, A is telling the truth because B is guilty and C is innocent,  C is telling the truth implies that B was not the killer which inturn imples that D was the killer and B was his accomplice.
So, we have found out that D was killer and B was accomplice.
We can rule out other cases if we want to:
iii) A and D are innocent---> A is telling the truth and B is guilty implies C is innocent, contradicting C is guilty
iv) B and C are innocent-->  A is lying which implies that B and C are guilty, contradicting B and C are innocent.
v) B and D are innocent--> A is lying which implies that B and C are guilty, contradicting B is innocent.
vi) C and D are innocent--> A is lying which implies that B and C are guilty, contradicting C is innocent.

So, A and C were innocent, D was killer and B was his accomplice.