Logic

[Kirti]

Sir, pls give detailed answer

Q) A chocolate bar has been stolen by either child A or B. One of A and B 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 & E are both right.
H : D & F are both right.
I : E or F is right, and may be both.
J : G or H is right, and may be both.
K: D and I are both 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?

[Amit Goyal]

Solution:
Assumption: Suppose C and L are telling the truth.
This implies that A has not stolen the chocolate bar. i.e. A is innocent.
And J is right (1) and K is wrong(2).
(1a) J is right implies G or H is right, and may be both
(2a) K is wrong implies D or I is wrong or may be both
(1b) G or H is right, and may be both implies D is right and E or F is right, and may be both.
(2b) D or I is wrong or may be both implies D is wrong or both E and F are wrong.
D is right and E or F is right, and may be both
And
D is wrong or both E and F are wrong.
cannot be true simultaneously.
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.