Answer to Question #204217 in Discrete Mathematics for Talha

Question

The police have three suspects for the murder of Janab Chaudary AllahDitta (Ch AD): Mr Chaloosak,Mr Maloosak and Mr Kabacha.

Chaloosak, Maloosak and Kabacha each declare that they did not kill Ch AD.

Chaloosak also states that Ch AD was a friend of Maloosak and that Kabacha disliked him.

Maloosak also states that he did not know Ch AD and that he was out of town the day Ch AD was killed.

Kabacha also states that he saw both Chaloosak and Maloosak with Ch AD the day of the killing and

that either Chaloosak or Maloosak must have killed him.

Can you determine who the murderer was if we know that:

a)one of the three men was guilty, the two innocent men are telling the truth, but the statement of guilty man may or may not be true?

b)innocent men do not lie?

Hint:

Translate the statements into logical expressions and reasoning from these expressions using

the truth tables.

Answer 1

Solution:

(a)

Given statements are:

St-1: Chaloosak, Maloosak and Kabacha each declare that they did not kill Ch AD.

St-2: Chaloosak also states that Ch AD was a friend of Maloosak and that Kabacha disliked him.

St-3: Maloosak also states that he did not know Ch AD and that he was out of town the day Ch AD was killed.

St-4: Kabacha also states that he saw both Chaloosak and Maloosak with Ch AD the day of the killing and that either Chaloosak or Maloosak must have killed him.

The possibilities are as follows:

Now, suppose Chaloosak is guilty, then statements of Maloosak and Kabacha are conflicting (Mal-oosak was out of town, and Kabacha saw Maloosak with Ch AD).

Suppose Kabacha is guilty, then statementso f Chaloosak and Maloosak are conflicting (Mal-

oosak is a friend of Ch AD, and Maloosak did not know Ch AD).

If Maloosak is guilty, then statements of Chaloosak and Kabacha are synched, and Maloosak

is also telling a lie

So, Maloosak killed Ch AD.

(b)

It is similar to part (a), except that we are not told ahead of time that one of them is guilty.

If all are innocent, then all of their statements are true, which is impossible.

Thus, there exists a possibility, where more than one are guilty.