logic questions(pls give full solution)

[ayushi]

Q2
a chocolate bar has been stolen by either child a or b. one of child is innocent .here are the statements of witnesses and other interested parties
C: a has not stolen the chocolate bar
D: a has stolen things in the past
E: b has stolen things in the past
f: e has stolen things in the past
g: d and e are bot right
h: d and f are both right
i: e or f is right , & may be both
j: g or h is right , and may be both
k: d and i are right
l: j is right and k is wrong

   suppose that c and l are either both telling the truth or both lying. who stole the chocolate bar?



Q3
one of a b c and d ha scommited a crime with the helpof another one of them. here the the tatements by the four individuals . the statements of the criminal and his accompalice are false and and those of the remaning 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 accomplince?

[Amit Goyal]

a chocolate bar has been stolen by either child a or b. one of child is innocent .here are the statements of witnesses and other interested parties
c: a has not stolen the chocolate bar
d: a has stolen things in the past
e: b has stolen things in the past
f: e has stolen things in the past
g: d and e are bot right
h: d and f are both right
i: e or f is right , & may be both
j: g or h is right , and may be both
k: d and i are right
l: j is right and k is wrong
suppose that c and l are either both telling the truth or both lying. who stole the chocolate bar?
Solution:
Assumption: Suppose c and l are telling the truth.
This implies a has not stolen the chocolate bar. i.e. a is innocent.
And j is right and k is wrong.
j is right implies g or h is right, and may be both
k is wrong implies d or i is wrong or may be both
g or h is right, and may be both implies d is right and e or f is right, and may be both.
d or i is wrong or may be both implies d is wrong or both e and f are wrong.
So we arrive at a contradiction.
Hence our assumption is false.
Thus, c and l are lying. This implies a has stolen the chocolate bar.

[Amit Goyal]

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.

[sohini]

sir, in the second question which deals with the killer and his accomplice C's statement is wrongly typed, it is C: If B was the killer, then D have had nothing to do with the crime. will the answer change now?

[Amit Goyal]

i did not look at the typed problem, i actually looked at the question papers while i solved this problem. so i have answered the problem that is given in the past year papers and not the one typed.

[RS]

Hi sir!
I want to practice these questions. Please recommend a good source (book/website) to practice these logic questions that are generally asked in jnu.
Also, please mention all reasoning and logic topics to be done for entrance examinations.